README.md

---
tags:
- sentence-transformers
- sentence-similarity
- feature-extraction
- generated_from_trainer
- dataset_size:892
- loss:MatryoshkaLoss
- loss:MultipleNegativesRankingLoss
base_model: Snowflake/snowflake-arctic-embed-l
widget:
- source_sentence: 'content=''1. What is the relationship between casting cooling
    rate and the formation of the Mg17A12 phase in the context of dynamic recrystallization
    (DRX)?\n2. How does the ANN model contribute to predicting hardness variations
    in AZ80 cast-forged I-beams under different casting and forging conditions?''
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  sentences:
  - 'denoises the data [82, 83, 84, 85]. During the forward process, the noise is
    added incrementally through numerous steps in a Markovian process:


    𝑞(𝑥𝑡|𝑥𝑡−1) ≔ 𝒩(𝑥𝑡; √1 − 𝛽𝑡𝑥𝑡−1, 𝛽𝑡𝑰)                                                                                                                                                                                             (3)


    Where 𝑥0 is a data sampled from the real data distribution 𝑞(𝑥) (i.e., 𝑥0 ∼ 𝑞(𝑥)).
    𝛽t ∈ (0,1) is the variance schedule (𝛽0 is small, and 𝛽T is large), and 𝑰 is the
    identity matrix. By using the notation 𝛼t ∶= 1 − 𝛽t and 𝛼t ∶= ∏st=0𝛼s, the noised
    data at any arbitrary step can be found:


    𝑞                                                                                         (𝑥t|𝑥t−1)
    ≔ 𝒩(𝑥t; √̅𝛼t𝑥0, (1 − 𝛼t)𝑰)                                                                                                 ̅                 (4)


    With reparameterization, 𝑥 can be written as:


    𝑥t = √̅𝛼t𝑥0 + √1 − 𝛼t𝝐                                                                                                                 ̅                                                                                                (5)


    Where 𝜖 ~ 𝒩(𝜖|0, 𝑰).


    During the backward process, the goal is to denoise images iteratively to get
    back to a less noisy version:


    𝑝                                                                                        (𝑥t−1|𝑥t)
    ≔ 𝒩(𝑥t−1; 𝜇t(𝑥t, 𝑡), 𝜎t𝑰)                                                                                       ̃                               (6)


    The reverse conditional shown in equation 6 does not have a closed form, but the
    following approximation is derived for that [82]:


    ̃𝜇t(𝑥t, 𝑡) ≈                                                        1                                                                                         𝛼t(𝑥t
    − √1−𝛼t                                                                      1−𝛼t𝜖t)            (7)


    Where 𝜖t is the noise introduced in the step 𝑡. The main idea is to learn this
    distribution, so we can denoise images by the reverse conditional. In order to
    do this, we train a neural network 𝜖𝜃(𝑥t, 𝑡) to approximate it:


    𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝐿(𝜃) = ‖𝜖t− 𝜖𝜃(𝑥t, 𝑡)‖2                                                                                                           2                                                                                             (8)


    In this work, a U-net architecture, which is first introduced by Ronneberger et
    al. [86] for image segmentation. Due to its symmetric down-sampling and up-sampling,
    this architecture is suitable for going from a noisy image to its equivalent denoised
    version. The encoding part consists of five blocks of max-pooling followed by
    several convolutional layers, group normalization, and GELU activation function.
    The self-attention mechanism with four heads is applied after each down-sampling
    layer. The decoding part is a somewhat mirrored structure of the encoding. It
    consists of five blocks, each one of them has bi-linear up-sampling followed by
    several convolutional layers, group normalization, and GELU activation function.
    The only difference is that after each up-sampling layer the data is concatenated
    with skip connections corresponding to channels with the same resolution from
    the encoding part. The model is conditioned on the time step by the Transformer
    positional embedding.


    38'
  - '# Figure 39


    SEM images of the different morphologies of the intermetallic compounds present
    in the cast-forged I-beams produced in the range of casting and forging conditions
    investigated in this study. a) Eutectic Mg17Al12, b) Lamellar Mg17Al12, c) Globular
    and Continuous Mg17Al12, and d) Intergranular Mg17Al12 and AlMn5. The casting
    cooling condition, forging temperature, and the location of each sample is depicted
    at the top right corner of each image.


    The microstructures of the I-beams exhibit significant variation due to different
    casting and forging conditions, as well as the evolution of Mg17Al12 phase. Figure
    40 and Figure 41 show the microstructures of the I-beams obtained from the web
    region and short flange, respectively, under different casting cooling rates and
    forging temperatures. Notably, the characteristics of DRX, including the extent
    of DRX, its distribution, and DRX grain size vary among the investigated samples.
    For the samples forged at 350°C, both the web region and short flange display
    a completely coverage of DRXed grains, indicating extensive recrystallization
    (see Figure 40a-b and Figure 41a-b). Conversely, a bimodal microstructure is observed
    in the remaining samples. At the web region of the samples forged at 250 and 300°C,
    the deformation and subsequent DRX has resulted in a distinctive “necklace” structure,
    characterized by initial elongated grains surrounded by DRXed grains (see Figure
    40c-f). At the short flange of the samples forged at 250 and 300°C, DRX is limited
    to the vicinity of the eutectic Mg17Al12 and the globular particles formed around
    them (see Figure 41c-f).'
  - '# Cooling Rate


    # Forging


    |Temperature|Measured|Predicted|Measured|Predicted|Measured|Predicted| | |

    |---|---|---|---|---|---|---|---|---|

    |250|47.58 + 2.70|46.31 + 1.69|47.50 + 2.59|47.56 + 2.34|43.73 + 3.29|44.01 +
    1.90|43.32 + 2.73|42.77 + 2.23|

    |NRMSE:|0.0501|0.0416| |0.0503| |0.0555| | |

    |300|40.63 + 2.25|39.93 + 1.42|40.48 + 2.19|41.82 + 1.90|38.80 + 2.63|39.27 +
    1.57|37.89 + 2.82|38.24 + 1.76|

    |NRMSE:|0.0468|0.0571| |0.0597| |0.0688| | |

    |350|35.46 + 3.12|33.89 + 1.49|34.75 + 2.69|35.49 + 1.78|34.16 + 2.16|32.94 +
    1.05|32.57 + 2.24|33.42 + 1.20|

    |NRMSE:|0.0933|0.0891| |0.0734| |0.0826| | |


    Figure 55: The predicted and actual contour maps and average HR30T hardness values
    with standard deviation for different combinations of the casting cooling rate
    and the forging temperature in the one-condition-out-scenario. NRMSE values for
    each prediction are also provided.


    The effect of the casting cooling rate is also related to the occurrence of DRX.
    Higher cooling rates result in finer α-Mg dendritic structure and prevent the
    formation of the lamellar Mg17A12 phase [127]. This can result in a more uniform
    distribution of the Mg17A12 intermetallic particles, which promote dynamic recrystallization
    by particle stimulated nucleation (PSN) mechanism [36]. Consequently, the samples
    forged from the casts with higher cooling rates can have more DRXed regions, resulting
    in slightly higher hardness.


    The ANN model accurately captures these hardness variations which are controlled
    by the evolution of several different microstructural features, even in prediction
    of completely unseen conditions. This model can be used in the range of studied
    casting and forging conditions to produce reliable hardness distribution contour
    maps and predict the average hardness of the AZ80 cast-forged I-beam.


    This model can be extended by including the effective local strain at each measurement
    point instead of the x and y coordinates of the measurement point, so that the
    model can be generalized for any arbitrary forged geometry. In addition, the casting
    cooling rate parameter can be replaced by a microstructure feature, such as secondary
    dendrite arm spacing (SDAS), to generalize the model for varied casting methods.
    On the other hand, the benefit of the current model is that it needs no further
    measurement or observation and produces hardness distribution contour maps from
    known processing parameters.'
- source_sentence: 'content=''1. What does a lower relative CRSS ratio indicate in
    terms of activation with reference to the basal slip?\n2. How does the initial
    texture affect material flow during deformation in AZ31 alloy?'' additional_kwargs={''refusal'':
    None} response_metadata={''token_usage'': {''completion_tokens'': 40, ''prompt_tokens'':
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  sentences:
  - '# 2.3.2 CRSS in the present case


    (b) relative CRSS ratio (lower values indicate an ease in activation with reference
    to the basal slip) [63]


    # Figures


    # Figure 2-12


    Effect of starting grain size on DRX fraction and DRX grain size in an extruded
    AZ31 alloy deformed in uniaxial compression at 300 °C, 0.01 s-1 to a strain of
    0.5. Adapted from [66]


    # Figure 2-13


    Effect of initial texture on material flow (a) symmetric distribution of the starting
    texture results in a symmetric material flow during deformation, (b) asymmetric
    distribution of starting texture with respect to compression direction (CD) results
    in a preferred material flow along ND. Deformation was done using symmetrical
    cylindrical samples (with cylindrical axis along the CD). CD: Compression direction,
    ND: Normal direction, TD: Transverse direction, ED: Extrusion direction. Adapted
    from [42]


    # Figure 2-14


    Effect of starting texture on (a) DRX fraction, (b) DRX grain size. AZ31 alloy
    deformed in plane strain compression, in temperature range of 300 °C– 400 °C,
    and strain rate range of 0.001 s-1 – 1 s-1. Adapted from [77]


    # Figure 2-15


    Effect of Al alloying in polycrystalline Mg on the CRSS for various deformation
    modes at: (a) Room temperature, (b) 200 °C. Twinning refer to {1012} tensile twinning.
    X-axis shows concentration of Al in square root of wt.% [82]


    # Figure 2-16


    Equilibrium phase fraction map of AZ80 alloy [93]


    # Figure 2-17


    Different Mg17Al12 precipitate morphologies in AZ alloys: (a) DP in lamellar form,
    (b) DP in ellipsoidal particle (globular) form, (c) CP in form of laths, and (d)
    CP in form of irregular plates. (a) and (b) are for AZ80 [92], while (c) and (d)
    are for AZ91 [91].


    # Figure 2-18


    (a-c) hot deformation of a cast-homogenized and pre-aged AZ91 sample at 300 °C,
    0.2 s-1, showing the occurrence of DRX only in regions previously occupied by
    DP [24]; (d-f) hot deformation of a cast-homogenized AZ91 sample at 400 °C, 0.2
    s-1. At 400 °C, CP got precipitated in the homogenized material during heating
    to and holding at the test temperature. (e-f) shows extensive DRX occurred in
    the material in this case as well [23]. (a) and (d) correspond to non-deformed
    samples, while (b, c, e, and f) correspond to deformed samples. C and D in (b)
    and (c) refer to continuous precipitates and discontinuous precipitates, respectively.


    # Figure 2-19


    Variation in (a) DRX ratio and (b) DRX grain size, with the Z parameter. Cast
    and extruded AZ31 alloys deformed in uniaxial compression for temperatures in
    the range of 300 - 450 °C, and strain rates in the range of 0.01 – 1 s-1. For
    the data presented in the graphs, DRXed grains were distinguished from the parent
    grains based on their size and shape [67].


    # Figure 2-20


    Change of DRX mechanism with deformation conditions for deformation of pure Mg.
    In area marked as I, DRX takes place via the twinning mechanism [35]'
  - '# 9.3.2. Microstructure to mechanical properties prediction model


    .......................................... 132


    # 9.3.3. Evaluation


    .........................................................................................................................
    133


    # 9.4. Results and discussion


    .............................................................................................................
    134


    # 9.4.1. Microstructure and quasi-static tensile test of the cast-forged AZ80
    magnesium alloy


    …134


    # 9.4.2. Comparison of data balancing strategies


    ........................................................................ 135


    # 9.4.3. Mechanical properties prediction


    ....................................................................................
    136


    # 9.5. Conclusion


    ...............................................................................................................................
    139


    # 10. Summary, Conclusions, limitations, and Future Work


    .......................................................... 141


    # 10.1. Summary


    ................................................................................................................................
    141


    # 10.2. Conclusions


    ............................................................................................................................
    141


    # 10.3. Limitations


    .............................................................................................................................
    145


    # References


    ...........................................................................................................................................
    148'
  - '# Characterization of forged magnesium alloys


    # 3.4 Case study


    In industrially forged parts, control of forging parameters, such as temperature
    and cooling rate is often challenging compared to laboratory-scale studies involving
    uniaxial compression. As a result, these variations can significantly impact the
    microstructure and texture development. Furthermore, industrial forgings typically
    exhibit larger dimensions and involve more complex material flow in closed dies
    further influencing the microstructure and texture development during forging.


    To exemplify these points, we refer to the work of Jahed et al. who studied the
    forging of an I-beam at the University of Waterloo by using a cast AZ31B alloy
    billet. The investigation served as a precursor study before the forging of a
    more geometrically complex automotive suspension component (Gryguc et al., 2021a,
    2021b, 2021c; Toscano et al., 2018a, 2018b; Williams et al., 2021). The geometry
    was forged using a starting cylindrical billet with a diameter of 63.5 mm and
    length of 65 mm machined from an original cast AZ31B billet of 300 mm diameter
    (Toscano et al., 2018a, 2018b).


    Forging was carried out using a 500-ton hydraulic press at 250 °C at a ram displacement
    rate of 20 mm/s, equivalent to an initial strain rate of about 0.3 s−1. The dies
    were pre-heated to the same forging temperature. Graphite was used as a lubricant.
    Forging was carried out in a single step. After forging, the forged part was allowed
    to cool by itself in the air. Subsequently, the part was longitudinally sectioned
    along mid-plane (refer to Fig. 36c) and prepared for metallographic examination
    using the standard practice. Microstructure and texture were observed at three
    different locations, as marked in Fig. 36c.


    The texture was measured using a Brucker D8 Discover diffractometer using the
    process outlined in Pahlevanpour et al. (2018) and presented here based on the
    (0002) basal pole figures. Surface hardness measurements on the entire prepared
    cross-section were carried out using a United True Blue II Rockwell Hardness Tester
    using Rockwell 15T scale and a 1/16 ball indenter.


    The results presented in Fig. 36 show significantly different microstructures
    and textures at the three locations marked in Fig. 36c. This difference is attributed
    to local variations in strain and strain rate gradients, which are significantly
    impacted by the die geometry as it constrains the material flow. Additionally,
    the DRX grain size from the microstructures presented here is coarser than what
    is expected from a specimen-size hot compression test, which can be attributed
    to a slow cooling rate post-forging (Beer and Barnett, 2008).


    The differences in microstructure and texture are also reflected in the variation
    in the hardness map presented in Fig. 36c. Gryguc et al., have shown that such
    spatial variations in microstructure and texture in a forged part also result
    in variations in strength and ductility (Gryguc et al., 2018). Other authors have
    also reported similar spatial variations in microstructure, texture, and mechanical
    properties in industrially relevant magnesium forged parts. Specifically, such
    variations were reported in aircraft brackets forged using AZ31 alloy and automotive
    wheel hubs forged using AZ80 alloy (Dziubińska et al., 2015; Liao et al., 2023).


    Due to these variations in mechanical properties, it is crucial to assess them
    individually in all critical load areas when forging a new part, rather than relying
    on single measurements assuming it represents the overall behavior of the bulk
    material.'
- source_sentence: 'content=''1. What was the purpose of using graphite lubricate
    on the die and billet during the forging process?  \n2. How were the tensile monotonic
    and fatigue test samples extracted from the closed die forged components?  ''
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  sentences:
  - 'microstructure at the end of the forging stage. Because of the I-beam geometry,
    the effective strain distribution is nonuniform across the forged sample. The
    middle part of the I-beam component, referred to as the web region, undergoes
    a higher extent of deformation [63, 39]. The grains are therefore severely elongated
    in the web region. The higher effective strain results in an increase in the hardness
    due to work hardening. Moreover, higher deformation promotes DRX, which refines
    grain size and further increases the material hardness.


    # Table 5: Chemical composition of the cast AZ80.


    |Element|Mg|Al|Zn|Cu|Fe|Mn|Ni|

    |---|---|---|---|---|---|---|---|

    |Wt.%|Bal.|8.64|0.52|0.0017|0.0044|0.24|0.0012|


    Figure 49: SEM microstructure images of the AZ80 magnesium alloy cast at a cooling
    rate of: a) 1.5 °C/s and b) 6 °C/s.


    Typical representative alterations in the forged microstructure due to casting
    and forging process parameters are shown in Figure 50. Depending on the forging
    temperature, some dissolution of the eutectic and precipitated Mg17Al12 phase
    might occur during forging. Figure 50a and Figure 50b compare the effect of forging
    temperature on the extent of dissolution of β-Mg17Al12 particles during forging
    for samples cast at 1.5 °C/s cooling rate and forged at 300 °C and 350 °C, respectively.
    Moreover, the Mg17Al12 intermetallic can precipitate in discontinuous and/or continuous
    morphologies [153]. Figure 50c and Figure 50d show two different morphologies
    of precipitated β-Mg17Al12 formed in samples cast at 6 °C/s cooling rate and forged
    at 250 °C and 300 °C, respectively. In addition to the direct effect of intermetallic
    compounds on the material hardness [146], the β-Mg17Al12 morphologies are shown
    to control microstructure evolution and hardness via affecting DRX [44].


    DRX occurs for all the studied cast-forge conditions; however, the extent and
    the size of DRXed grains vary for different samples. Both eutectic and precipitated
    Mg17Al12, as well as the higher amount of deformation promote DRX [44]. The size
    of DRXed grains is also controlled by deformation temperature [36] and the presence
    of fine intermetallic particles. Figure 50e and Figure 50f illustrate the effect
    of deformation temperature on the grain size of DRXed grains. Forging the sample
    cast at 1.5'
  - 'Metals 2021, 11, 1290 lower control arm (step 4). Graphite lubricate was used
    on the die and billet to reduce friction, sticking and promote material flow.
    The orientation of the billet to the press was such that the radial direction
    was along the direction of the press stroke (i.e., the direction of forging was
    parallel to the radial direction of the billet). Forging was carried out in a
    single step at a displacement rate of 2.1–4.2 mm/s, and they were allowed to air
    cool with no additional post-heat treatments.


    # Figure 1. Plan view of extruded billet during different stages of forging operation
    to achieve final component (prior to machining of the flash).


    Tensile monotonic and fatigue test samples were utilized with geometries according
    to Roostaei et al. [25] and a 4 mm thickness, these were machined from various
    locations throughout closed die forged components. There were 18 test samples
    that were extracted from 18 different locations throughout each of the closed
    die forging (see Figure 2), all with varying thermomechanical histories. One component
    forged at each temperature was dedicated to stress-controlled fatigue testing
    where 10 samples are presented for the 300 °C forging and 8 for the 450 °C forging.
    Strain-controlled tests were performed on 14 different samples extracted from
    another component forged at 300 °C. The remainder of the original 18 test samples
    from each component were used for monotonic testing to understand the spatial
    variation in strength and ductility. The test samples had a nominal surface finish
    of Ra ≤ 0.2 μm; however, in practice, the actual roughness was substantially less,
    around 0.05 μm. These samples were later utilized for quasi-static and cyclic
    (stress-controlled) testing.


    The quasi-static tensile tests were performed according to ASTM standard E8/E8M-15a
    using an MTS 810 Servo-Hydraulic test machine operating in displacement control
    mode with a displacement rate of 1 mm/min. Strain measurement was accomplished
    using a GOM ARAMIS 3D 5MP DIC system which passively functioned to measure the
    average axial strain on the surface of the gauge section of the sample throughout
    the duration of the test. The fatigue tests were performed as per ASTM E466-15
    in an ambient environment using an MTS 810 Servo-Hydraulic test machine operating
    in stress control mode at a frequency range of 0.5 Hz to 60 Hz depending on the
    stress amplitude to maintain an approximately consistent loading rate between
    all tests.


    The strain was measured throughout the first 10,000 cycles using an MTS 632.26
    extensometer with an 8-mm gauge and travel of ±1.2 mm until stabilization of the
    cyclic hysteresis loop was achieved. The tests were conducted at zero mean stress
    (i.e., RL = −1, fully reversed stress cycle) and stress amplitudes of between
    140 MPa and 180 MPa. The failure criteria for the tests were considered to be
    the final rupture of the specimen gauge section.


    # Figure 2. Sample extraction schematic from AZ80 Mg die-forged component.


    # 3. Results and Discussion


    # 3.1. Structure-Property Relationship (Effect of Material Modification)


    Some of the favourable aspects of selecting forging as a “near net-shape” manufacturing
    process include...'
  - 'The effect of initial cooling rate is apparent. Material cast with a higher cooling
    rate shows a higher peak compressive stress than material cast with a lower cooling
    rate, though this effect is most noticeable at low temperatures and/or high strain
    rates. Following the peak stress, the HCR samples experienced a higher rate of
    dynamic softening, lowering the stress to a similar value as the LCR samples.
    At high strains, after significant deformation has occurred, there is no effect
    of initial cast cooling rate. The peak compressive stress of all deformation conditions
    that were tested is shown in Figure 30. While some conditions show a higher difference
    in peak stress than others, the effect is consistent across all temperatures and
    strain rates. The higher flow stress that is seen in finer grained cast AZ80 has
    also been reported for similar alloys [100, 101].


    |a)| |250 C-HCR|b)|I/s-HCR| |

    |---|---|---|---|---|---|

    |200| |250 C-LCR|200|I/s-LCR| |

    |180|300°C-HCR|180| |0.1/s-HCR| |

    | |300°C-LCR| | |0.1/s-LCR| |

    |160| |350 C-HCR|60|0.01/s-HCR| |

    | | |350 C-LCR| |0.01/s-LCR| |

    |140| | |9|140| |

    |8|120| |3|120| |

    |2|80|2|80| | |

    |60| |60| | | |

    |40| |40| | | |

    |20| |20| | | |

    |0.0|0.2|0.4|0.6|0.8|1.0|


    Figure 29: Measured compressive flow curves for degassed AZ80 cast with cooling
    rates of 3.4°C/s (LCR, dashed line) and 24.7°C/s (HCR, solid line) showing: a)
    the effect of temperature at a strain rate of 0.1s-1 and b) the effect of strain
    rate at a temperature of 300°C. Data from [78].


    |250C-HCR|220|250C-LCR|

    |---|---|---|

    |300 C-HCR|200|300C-LCR|

    |350C-HCR|180|350C-LCR|

    |3|160| |

    |2|120| |

    |2|100| |

    |80| | |

    |0.01| | |


    Figure 30: Peak compressive stress at each strain rate for LCR and HCR degassed
    AZ80 at deformation temperatures of 250°C, 300°C, and 350°C. Data from [78].


    52'
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    the texture modification due to forging in AZ80 Mg materials?\n2. How does the
    forging temperature affect the yield strength of AZ80 Mg according to the studies
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    ''fp_7fcd609668'', ''finish_reason'': ''stop'', ''logprobs'': None} id=''run-36dd8d40-0259-4d26-8db7-9eb705f3210d-0''
    usage_metadata={''input_tokens'': 855, ''output_tokens'': 49, ''total_tokens'':
    904, ''input_token_details'': {''audio'': 0, ''cache_read'': 0}, ''output_token_details'':
    {''audio'': 0, ''reasoning'': 0}}'
  sentences:
  - 'Metals 2021, 11, 1290


    (T5) treatment, with promising results [30]. In general, a significant component
    of the variability observed in the properties of the as-forged components stems
    from the air-cooling following forging, and the resulting variability in local
    cooling rates throughout the components. They also mention that the second phase
    sizes and morphologies which precipitate are highly dependent on the temperature
    and aging time, and in this study since air cooling was employed, both of these
    parameters would naturally spatially vary throughout the forged component and
    would be different in location #3 (Figure 8a) and location #13 (Figure 8b). Supporting
    this, is the observation that there is an apparent difference in the uniformity
    of the distribution in these continuous precipitates between the two locations.
    In location #3 (Figure 8a) the precipitate distribution is somewhat striated in
    the middle of the micrograph, with a non-uniform volume fraction of the second
    phase, as compared with location #13 (Figure 8b) which is much more uniform in
    nature across the entire image. Furthermore, from the higher magnification images,
    it can be observed that, in general, location #3 (Figure 8c) has comparatively
    larger precipitate sizes relative to location #13 (Figure 8d). A more refined
    precipitate structure with smaller spacing between particles leads to a higher
    propensity to resist dislocation movement when plastically deformed which is beneficial
    to the mechanical properties [34]. Both effects of this increase in uniformity
    in precipitation distribution and decrease in size in location #13 (Figure 8b)
    can contribute to an increase in strength, and fatigue life (as observed in the
    two samples tested at 160 MPa where there is a difference in life of about 6×)
    [1,34]. The source of this variation in life has many contributing effects, the
    most significant of which are: firstly, the effect of the thermal process history
    on the microstructure and precipitate morphology discussed here; secondly, the
    equivalent strain imposed by the mechanical deformation during forging which will
    be subsequently discussed; and finally, the well documented stochastic nature
    of fatigue.


    |T = 450 °C|y = 568.63x-0.13|

    |---|---|

    |T = 300 °C|y = 429.9x-0.088|


    [MPa]


    Amplitude cycles


    Stress


    Number of Cycles to Failure [N]


    |5,000|50,000|500,000|

    |---|---|---|

    |160|170|#13: 282,092|

    |140|130|#3: 46,428|


    Figure 7. Relationship between the forging temperature and stress-controlled fatigue
    behaviour for closed-die forged AZ80 Mg automotive suspension component. Location
    #3 & #13 are highlighted for reference (per Figure 2) as they are subsequently
    referred to in the SEM micrographs in Figure 8.


    Figure 8 illustrates SEM micrographs highlighting the precipitate morphology of
    two different locations within the forging that were tested at the same stress
    amplitude yet exhibited a significantly different number of cycles to failure.
    The precipitates are continuous in nature and range in both size and morphology,
    from smaller lozenge/blunted asymmetric hexagonal structure to larger slab-like
    structures, and they can be observed in the brighter contrast regions in the micrographs
    with the darker background being the.'
  - '# Chapter 4: Methodology


    Due to a relatively coarse grain size of the as-received cast material (compared
    to the starting extruded material), a larger area needed to be scanned for the
    cast-deformed samples, to be able to capture enough grains to produce statistically
    relevant results. Details of the area scanned for cast and extruded-deformed samples
    at various strain levels are provided in Figure 4-16. Note that for the sample
    deformed to the strain of 1.0, the scan area was limited to 0.75 x 0.6 mm even
    for the cast material, in order to avoid an overlap of the scan area with the
    dead metal zone (refer to Figure 4-16 (c) and (d)). As the results in later text
    show, hot deformation resulted in a considerable grain refinement in both cast
    and extruded materials, and this relatively small scan area was still found to
    adequately capture statistically relevant amount of data.


    |(a)|8 = 0.15|(b)|8 = 0.4|(c)|8 = 1.0|

    |---|---|---|---|---|---|

    |8|3 0.75 mm|!|8 0.75 mm|0.75 mm| |

    | |LQ|LO| | | |

    | | |(d)|17.5 mm|E| |

    |0 0.75 mm 2mm| | | | | |

    |Cast Az80 = 4008C, 0.1s-1 8 = 1.0| | | | | |

    |EBSD mapping area for cast mt| | | | | |

    |EBSD mapping area for extruded mt; Dead metal zone| | | | | |


    Figure 4-16 Location and size of EBSD scan for cast and extruded compressed samples.
    Sample size and the scan area are proportionally scaled. The dead metal zone location
    and extent is a simple schematic (and not to scale) and just for illustrative
    purposes. The true extent of the dead metal zone for one of the samples can be
    visualized from (d).


    The scanned data was processed and analysed using TSL OIM 8.0 software. The data
    was cleaned using standard data cleaning techniques [122]. This is illustrated
    through Figure 4-17 and Figure 4-18 for an extruded AZ80 sample deformed at 400
    °C, 0.1 s-1 to a strain of 1.0. Initially, based on Image Quality (IQ) map and
    distribution, it was observed that areas with precipitates showed much lower IQ
    values. Therefore, the data pertaining to the precipitates could be filtered away
    from the data pertaining to the actual grains, using a lower threshold on the
    IQ values. For the case presented in Figure 4-17, an IQ value of 550 was found
    to be appropriate, though it should be noted.'
  - 'dominated by compressive loading) on the resulting texture of the as-forged material
    was previously explored by Grygu´c et al. [16, 17] in medium-scale I-beam style
    forgings. Those studies concluded that the favourable texture modification due
    to forging was the alignment of the c-axis of the hexagonal-closed-packed (HCP)
    crystal to be parallel with the local forging direction (or direction of dominant
    compressive loading), which is often normal to the die surface in relatively thin
    forgings at areas closer to the surface of the forged component. Depending on
    the process temperature, and local thermal history (accounting for the heat of
    deformation), the material recrystallization process may be highly non-uniform
    and heterogeneous in nature, resulting in spatially varying microstructure, texture
    and thus mechanical properties.


    # Figure 6


    illustrates the relationship between the primary thermal process parameter (the
    target forging temperature) and the resulting yield strength for a variety of
    forged AZ80 Mg. Similar AZ80 Mg material conditions are presented, cast [3], extruded
    [17], cast-forged [3] and extruded forged [17], and they are once again grouped
    into categories of starting microstructure for clarity in illustrating the process-property
    relationship of forged AZ80 Mg. It can be observed that there is a general trend
    (albeit it, quite weak) where lower forging temperatures produce material with
    higher strength. This relatively poor correlation will subsequently be discussed
    in relation to the recrystallization mechanisms present during the forging process.
    For wrought forms of base material (i.e., extruded), forging at higher temperatures
    can result in grain growth (resulting in lower strength) and lower temperatures
    the potential for shear cracking (from reduced ductility) [30]. Of the studies
    presented, all were isothermal in nature (forging dies and billet are at the same
    temperature), and the forging temperature window ranges 250–450 °C. Beneath 250
    °C, edge cracking and poor formability result as only a few deformation mechanisms
    become active, and large strain is not achievable [31]. At temperatures higher
    than 427 °C, incipient melting of the Mg17Al12 eutectic phase will occur near
    the grain boundary [13, 32]. This propensity towards incipient melting at higher
    processing temperatures for AZ series Mg alloys limits them from being extruded
    quickly, as compared to other structural metals, the processing window is quite
    narrow; however, this is not as limiting with die forging as the local deformation
    rates are typically smaller [33]. Chaudhury et al. suggest for AZ80 Mg, a non-isothermal
    forging process with a temperature window of 290–400 °C for the billet, and 205–290
    °C for the forging dies to avoid these aforementioned types of defects that can
    result in the as-forged material [30] which agrees well with the trend seen in
    the current study.


    |Forging Temperature [°C]|Yield Strength|

    |---|---|

    |300|280|

    |260|240|

    |220|200|

    |180|160|

    |140|120|

    |100| |


    Figure 6. Relationship between primary thermal process parameter (forging temperature)
    and resulting yield strength of AZ80 Mg after forging (subdivided into various
    starting material conditions). The current study denotes properties extracted
    from various locations of the extruded then die-forged automotive suspension control
    arm forged at various temperatures (300 °C and 450 °C). For reference, extruded-forged
    data can found in the following studies [5–13,16], cast-forged from [3,16].


    The stress-controlled fatigue response of the closed-die forged AZ80 Mg automotive
    suspension component is illustrated in Figure 7 for the two target forging temperatures
    that were investigated in this current study. It can be easily observed that for
    virtually all of the tests performed, for a given stress amplitude, the lower
    forging temperature (300 °C) pro-'
- source_sentence: 'content=''1. What does MSE stand for in the context provided?\n2.
    Which technique is abbreviated as OES?'' additional_kwargs={''refusal'': None}
    response_metadata={''token_usage'': {''completion_tokens'': 24, ''prompt_tokens'':
    196, ''total_tokens'': 220, ''completion_tokens_details'': {''accepted_prediction_tokens'':
    0, ''audio_tokens'': 0, ''reasoning_tokens'': 0, ''rejected_prediction_tokens'':
    0}, ''prompt_tokens_details'': {''audio_tokens'': 0, ''cached_tokens'': 0}}, ''model_name'':
    ''gpt-4o-mini-2024-07-18'', ''system_fingerprint'': ''fp_709714d124'', ''finish_reason'':
    ''stop'', ''logprobs'': None} id=''run-798f8f65-4b52-4198-a267-dc6f61a192d0-0''
    usage_metadata={''input_tokens'': 196, ''output_tokens'': 24, ''total_tokens'':
    220, ''input_token_details'': {''audio'': 0, ''cache_read'': 0}, ''output_token_details'':
    {''audio'': 0, ''reasoning'': 0}}'
  sentences:
  - '# References


    1. J.-H. Jun, "Dependence of hardness on interlamellar spacing of discontinuous
    precipitates in cast AZ91 magnesium alloy," Journal of Alloys and Compounds, vol.
    725, pp. 237-241, 2017.

    2. H. Jafari, M.H. Idris, A. Ourdjini, and G. Payganeh, "Effect of thermomechanical
    treatment on microstructure and hardness behavior of AZ63 magnesium alloy," Acta
    Metallurgica Sinica, vol. 22, pp. 401-407, 2009.

    3. Fuan Wei, Zhengang Zhang, Bo Shi, Chen Yang, and Jinhui Wang, "Effect of rolling
    deformation on microstructure and mechanical properties of Mg-6Sn-3Al-1Zn alloy,"
    Materials Research Express, vol. 7, p. 026516, 2020.

    4. Ondřej Hilšer, Stanislav Rusz, Pavel Szkandera, Lubomír Čížek, Martin Kraus,
    Jan Džugan, and Wojciech Maziarz, "Study of the Microstructure, Tensile Properties
    and Hardness of AZ61 Magnesium Alloy Subjected to Severe Plastic Deformation,"
    Metals, vol. 8, p. 776, 2018.

    5. Longqing Tang, Guowei Bo, Fulin Jiang, Shiwei Xu, Jie Teng, Dingfa Fu, Hui
    Zhang, "Unravelling the precipitation evolutions of AZ80 magnesium alloy during
    non-isothermal and isothermal processes," Journal of Materials Science & Technology,
    vol. 75, pp. 184-195, 2021.

    6. Aditya Ramesh, Prafulla Dhariwal, Alex Nichol, Casey Chu, Mark Chen, "Hierarchical
    text-conditional image generation with clip latents," arXiv preprint arXiv:2204.06125,
    p. https://doi.org/10.48550/arXiv.2204.06125, 2022.

    7. P. Acar, "Machine Learning Approach for Identification of Microstructure–Process
    Linkages," AIAA Journal, vol. 57, no. 8, pp. 3608-3614; https://doi.org/10.2514/1.J058244,
    2019.

    8. Yanming Liu, Shu Jian Chen, Kwesi Sagoe-Crentsil, Wenhui Duan, "Large set microstructure
    reconstruction mimicking quantum computing approach via deep learning," Acta Materialia,
    vol. 230, p. 117860; https://doi.org/10.1016/j.actamat.2022.117860, 2022.

    9. Yue Liu, Tianlu Zhao, Wangwei Ju, Siqi Shi, "Materials discovery and design
    using machine learning," Journal of Materiomics, vol. 3, no. 3, pp. 159-177; https://doi.org/10.1016/j.jmat.2017.08.002,
    2017.

    10. Brian L. DeCost, Toby Francis, Elizabeth A. Holm, "Exploring the microstructure
    manifold: Image texture representations applied to ultrahigh carbon steel microstructures,"
    Acta Materialia, vol. 133, pp. 30-40; https://doi.org/10.1016/j.actamat.2017.05.014,
    2017.

    11. Daniel A. Cogswell and W. Craig Carter, "Thermodynamic phase-field model for
    microstructure with multiple components and phases: The possibility of metastable
    phases," Phys. Rev. E, vol. 83, no. 6, p. 061602; https://doi.org/10.1103/PhysRevE.83.061602,
    2011.

    12. S. Florez, M. Shakoor, T. Toulorge, M. Bernacki, "A new finite element strategy
    to simulate microstructural evolutions," Computational Materials Science, vol.
    172, p. 109335; https://doi.org/10.1016/j.commatsci.2019.109335, 2020.

    13. Damien Tourret, Hong Liu, Javier LLorca, "Phase-field modeling of microstructure
    evolution: Recent applications, perspectives and challenges," Progress in Materials
    Science, vol. 123, p. 100810; https://doi.org/10.1016/j.pmatsci.2021.100810, 2022.'
  - '# MSE – Mean Squared Error


    # NRMSE – Normalized Root Mean Squared Error


    # OES – Optical Emission Spectrometry


    # PSN – Particle Stimulated Nucleation


    # ReLU – Rectified linear unit


    # RT – Room Temperature


    # SDAS – Secondary Dendrite Arm Spacing


    # SEM – Scanning Electron Microscopy


    # SGD – Stochastic Gradient Descent


    # SVM – Support Vector Machine


    # TD – Transverse Direction


    # UTS – Ultimate Tensile Strength


    # VAE – Variational Autoencoder


    # XCT – X-ray Computed Tomography


    # YS – Yield Strength


    # xxi'
  - 'analytical or even empirical model that could relate a specific process parameter
    to a selected property. Also, compared to steel or aluminum alloys, there are
    still not enough experimental results that guide researchers and manufacturers
    in selecting proper processing routes and finding the optimum combination of process
    parameters.


    Machine learning techniques, as computational tools that use data gathered from
    experience to improve performance, have shown to be successful in establishing
    such relationships between interacting variables. Machine learning methods can
    be used to connect sparse findings on production of magnesium alloys to provide
    some insight into missing pieces of information. Such a link between different
    parameters not only help researchers to predict desired properties or select optimum
    parameters, but also can be used in theoretical studies of controlling mechanisms,
    which can finally give rise to more robust analytical or empirical models.


    In the current study, the feasibility of using machine learning approaches in
    establishing process-microstructure-property relationship would be put to the
    test. For this purpose, cast-forging process of AZ80 magnesium alloy, as a cost-effective
    hybrid manufacturing method, is going to be studied through advanced characterization
    methods. The effect of different process parameters of casting, forging, and intermediate
    thermo-mechanical processes and microstructural and mechanical properties of material
    in various stages of manufacturing are parameters of interest which will also
    be linked through machine learning models.


    # 1.2 Challenges and Opportunities


    To establish a link between process, microstructure, and property, a complete
    study of all the controlling parameters is required. Previous studies on the viability
    of production of magnesium-based structural components cover a variety of parameters
    and properties [3,4,7,8], but since these studies have focused on different aspects
    of production, a complete experimental study on the effect of parameters of casting
    and forging processes for AZ80 magnesium alloy is selected as a basis for the
    establishment of this relationship. It also contributes to broadening the knowledge
    of cast-forging manufacturing of magnesium alloys, where thorough experimental
    work is unavailable.


    Such an experimental study allows us to measure all properties in a controlled,
    consistent approach, while it also allows us to incorporate different processing
    parameters and, if necessary, append new variables based on the performance of
    machine learning models.


    As the experimental part progresses through different processing steps like wedge
    casting, cylinder casting, homogenization, I-beam forging, optimized preform casting,
    and forging the final structural components, data-driven models are developed
    to link process parameters to microstructural features.'
pipeline_tag: sentence-similarity
library_name: sentence-transformers
metrics:
- cosine_accuracy@1
- cosine_accuracy@3
- cosine_accuracy@5
- cosine_accuracy@10
- cosine_precision@1
- cosine_precision@3
- cosine_precision@5
- cosine_precision@10
- cosine_recall@1
- cosine_recall@3
- cosine_recall@5
- cosine_recall@10
- cosine_ndcg@10
- cosine_mrr@10
- cosine_map@100
model-index:
- name: SentenceTransformer based on Snowflake/snowflake-arctic-embed-l
  results:
  - task:
      type: information-retrieval
      name: Information Retrieval
    dataset:
      name: Unknown
      type: unknown
    metrics:
    - type: cosine_accuracy@1
      value: 0.9948979591836735
      name: Cosine Accuracy@1
    - type: cosine_accuracy@3
      value: 1.0
      name: Cosine Accuracy@3
    - type: cosine_accuracy@5
      value: 1.0
      name: Cosine Accuracy@5
    - type: cosine_accuracy@10
      value: 1.0
      name: Cosine Accuracy@10
    - type: cosine_precision@1
      value: 0.9948979591836735
      name: Cosine Precision@1
    - type: cosine_precision@3
      value: 0.33333333333333337
      name: Cosine Precision@3
    - type: cosine_precision@5
      value: 0.19999999999999998
      name: Cosine Precision@5
    - type: cosine_precision@10
      value: 0.09999999999999999
      name: Cosine Precision@10
    - type: cosine_recall@1
      value: 0.9948979591836735
      name: Cosine Recall@1
    - type: cosine_recall@3
      value: 1.0
      name: Cosine Recall@3
    - type: cosine_recall@5
      value: 1.0
      name: Cosine Recall@5
    - type: cosine_recall@10
      value: 1.0
      name: Cosine Recall@10
    - type: cosine_ndcg@10
      value: 0.9981169885386298
      name: Cosine Ndcg@10
    - type: cosine_mrr@10
      value: 0.9974489795918368
      name: Cosine Mrr@10
    - type: cosine_map@100
      value: 0.9974489795918368
      name: Cosine Map@100
---

# SentenceTransformer based on Snowflake/snowflake-arctic-embed-l

This is a [sentence-transformers](https://www.SBERT.net) model finetuned from [Snowflake/snowflake-arctic-embed-l](https://huggingface.co/Snowflake/snowflake-arctic-embed-l). It maps sentences & paragraphs to a 1024-dimensional dense vector space and can be used for semantic textual similarity, semantic search, paraphrase mining, text classification, clustering, and more.

## Model Details

### Model Description
- **Model Type:** Sentence Transformer
- **Base model:** [Snowflake/snowflake-arctic-embed-l](https://huggingface.co/Snowflake/snowflake-arctic-embed-l) <!-- at revision d8fb21ca8d905d2832ee8b96c894d3298964346b -->
- **Maximum Sequence Length:** 512 tokens
- **Output Dimensionality:** 1024 dimensions
- **Similarity Function:** Cosine Similarity
<!-- - **Training Dataset:** Unknown -->
<!-- - **Language:** Unknown -->
<!-- - **License:** Unknown -->

### Model Sources

- **Documentation:** [Sentence Transformers Documentation](https://sbert.net)
- **Repository:** [Sentence Transformers on GitHub](https://github.com/UKPLab/sentence-transformers)
- **Hugging Face:** [Sentence Transformers on Hugging Face](https://huggingface.co/models?library=sentence-transformers)

### Full Model Architecture

```
SentenceTransformer(
  (0): Transformer({'max_seq_length': 512, 'do_lower_case': False}) with Transformer model: BertModel 
  (1): Pooling({'word_embedding_dimension': 1024, 'pooling_mode_cls_token': True, 'pooling_mode_mean_tokens': False, 'pooling_mode_max_tokens': False, 'pooling_mode_mean_sqrt_len_tokens': False, 'pooling_mode_weightedmean_tokens': False, 'pooling_mode_lasttoken': False, 'include_prompt': True})
  (2): Normalize()
)
```

## Usage

### Direct Usage (Sentence Transformers)

First install the Sentence Transformers library:

```bash
pip install -U sentence-transformers
```

Then you can load this model and run inference.
```python
from sentence_transformers import SentenceTransformer

# Download from the 🤗 Hub
model = SentenceTransformer("tabesink92/mg_alloy-snowflake-arctic-embed-l-ft-v2")
# Run inference
sentences = [
    "content='1. What does MSE stand for in the context provided?\\n2. Which technique is abbreviated as OES?' additional_kwargs={'refusal': None} response_metadata={'token_usage': {'completion_tokens': 24, 'prompt_tokens': 196, 'total_tokens': 220, 'completion_tokens_details': {'accepted_prediction_tokens': 0, 'audio_tokens': 0, 'reasoning_tokens': 0, 'rejected_prediction_tokens': 0}, 'prompt_tokens_details': {'audio_tokens': 0, 'cached_tokens': 0}}, 'model_name': 'gpt-4o-mini-2024-07-18', 'system_fingerprint': 'fp_709714d124', 'finish_reason': 'stop', 'logprobs': None} id='run-798f8f65-4b52-4198-a267-dc6f61a192d0-0' usage_metadata={'input_tokens': 196, 'output_tokens': 24, 'total_tokens': 220, 'input_token_details': {'audio': 0, 'cache_read': 0}, 'output_token_details': {'audio': 0, 'reasoning': 0}}",
    '# MSE – Mean Squared Error\n\n# NRMSE – Normalized Root Mean Squared Error\n\n# OES – Optical Emission Spectrometry\n\n# PSN – Particle Stimulated Nucleation\n\n# ReLU – Rectified linear unit\n\n# RT – Room Temperature\n\n# SDAS – Secondary Dendrite Arm Spacing\n\n# SEM – Scanning Electron Microscopy\n\n# SGD – Stochastic Gradient Descent\n\n# SVM – Support Vector Machine\n\n# TD – Transverse Direction\n\n# UTS – Ultimate Tensile Strength\n\n# VAE – Variational Autoencoder\n\n# XCT – X-ray Computed Tomography\n\n# YS – Yield Strength\n\n# xxi',
    'analytical or even empirical model that could relate a specific process parameter to a selected property. Also, compared to steel or aluminum alloys, there are still not enough experimental results that guide researchers and manufacturers in selecting proper processing routes and finding the optimum combination of process parameters.\n\nMachine learning techniques, as computational tools that use data gathered from experience to improve performance, have shown to be successful in establishing such relationships between interacting variables. Machine learning methods can be used to connect sparse findings on production of magnesium alloys to provide some insight into missing pieces of information. Such a link between different parameters not only help researchers to predict desired properties or select optimum parameters, but also can be used in theoretical studies of controlling mechanisms, which can finally give rise to more robust analytical or empirical models.\n\nIn the current study, the feasibility of using machine learning approaches in establishing process-microstructure-property relationship would be put to the test. For this purpose, cast-forging process of AZ80 magnesium alloy, as a cost-effective hybrid manufacturing method, is going to be studied through advanced characterization methods. The effect of different process parameters of casting, forging, and intermediate thermo-mechanical processes and microstructural and mechanical properties of material in various stages of manufacturing are parameters of interest which will also be linked through machine learning models.\n\n# 1.2 Challenges and Opportunities\n\nTo establish a link between process, microstructure, and property, a complete study of all the controlling parameters is required. Previous studies on the viability of production of magnesium-based structural components cover a variety of parameters and properties [3,4,7,8], but since these studies have focused on different aspects of production, a complete experimental study on the effect of parameters of casting and forging processes for AZ80 magnesium alloy is selected as a basis for the establishment of this relationship. It also contributes to broadening the knowledge of cast-forging manufacturing of magnesium alloys, where thorough experimental work is unavailable.\n\nSuch an experimental study allows us to measure all properties in a controlled, consistent approach, while it also allows us to incorporate different processing parameters and, if necessary, append new variables based on the performance of machine learning models.\n\nAs the experimental part progresses through different processing steps like wedge casting, cylinder casting, homogenization, I-beam forging, optimized preform casting, and forging the final structural components, data-driven models are developed to link process parameters to microstructural features.',
]
embeddings = model.encode(sentences)
print(embeddings.shape)
# [3, 1024]

# Get the similarity scores for the embeddings
similarities = model.similarity(embeddings, embeddings)
print(similarities.shape)
# [3, 3]
```

<!--
### Direct Usage (Transformers)

<details><summary>Click to see the direct usage in Transformers</summary>

</details>
-->

<!--
### Downstream Usage (Sentence Transformers)

You can finetune this model on your own dataset.

<details><summary>Click to expand</summary>

</details>
-->

<!--
### Out-of-Scope Use

*List how the model may foreseeably be misused and address what users ought not to do with the model.*
-->

## Evaluation

### Metrics

#### Information Retrieval

* Evaluated with [<code>InformationRetrievalEvaluator</code>](https://sbert.net/docs/package_reference/sentence_transformer/evaluation.html#sentence_transformers.evaluation.InformationRetrievalEvaluator)

| Metric              | Value      |
|:--------------------|:-----------|
| cosine_accuracy@1   | 0.9949     |
| cosine_accuracy@3   | 1.0        |
| cosine_accuracy@5   | 1.0        |
| cosine_accuracy@10  | 1.0        |
| cosine_precision@1  | 0.9949     |
| cosine_precision@3  | 0.3333     |
| cosine_precision@5  | 0.2        |
| cosine_precision@10 | 0.1        |
| cosine_recall@1     | 0.9949     |
| cosine_recall@3     | 1.0        |
| cosine_recall@5     | 1.0        |
| cosine_recall@10    | 1.0        |
| **cosine_ndcg@10**  | **0.9981** |
| cosine_mrr@10       | 0.9974     |
| cosine_map@100      | 0.9974     |

<!--
## Bias, Risks and Limitations

*What are the known or foreseeable issues stemming from this model? You could also flag here known failure cases or weaknesses of the model.*
-->

<!--
### Recommendations

*What are recommendations with respect to the foreseeable issues? For example, filtering explicit content.*
-->

## Training Details

### Training Dataset

#### Unnamed Dataset

* Size: 892 training samples
* Columns: <code>sentence_0</code> and <code>sentence_1</code>
* Approximate statistics based on the first 892 samples:
  |         | sentence_0                                                                            | sentence_1                                                                           |
  |:--------|:--------------------------------------------------------------------------------------|:-------------------------------------------------------------------------------------|
  | type    | string                                                                                | string                                                                               |
  | details | <ul><li>min: 340 tokens</li><li>mean: 371.01 tokens</li><li>max: 410 tokens</li></ul> | <ul><li>min: 29 tokens</li><li>mean: 439.26 tokens</li><li>max: 512 tokens</li></ul> |
* Samples:
  | sentence_0                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        | sentence_1                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   |
  |:--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|:---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
  | <code>content='1. What experimental method was used to investigate the fatigue properties of extruded AZ80 magnesium alloys in the study?  \n2. How does the crack initiation mechanism change with varying stress amplitudes in the AZ80 magnesium alloys?' additional_kwargs={'refusal': None} response_metadata={'token_usage': {'completion_tokens': 46, 'prompt_tokens': 731, 'total_tokens': 777, 'completion_tokens_details': {'accepted_prediction_tokens': 0, 'audio_tokens': 0, 'reasoning_tokens': 0, 'rejected_prediction_tokens': 0}, 'prompt_tokens_details': {'audio_tokens': 0, 'cached_tokens': 0}}, 'model_name': 'gpt-4o-mini-2024-07-18', 'system_fingerprint': 'fp_7fcd609668', 'finish_reason': 'stop', 'logprobs': None} id='run-d649e508-ccc4-420e-b812-67719c92f2cb-0' usage_metadata={'input_tokens': 731, 'output_tokens': 46, 'total_tokens': 777, 'input_token_details': {'audio': 0, 'cache_read': 0}, 'output_token_details': {'audio': 0, 'reasoning': 0}}</code> | <code># Fatigue behaviour and fractography of extruded AZ80 magnesium alloys in very high cycle regime<br><br># Kazuaki Shiozawaa *, Tomoki Kashiwagi b, Tutomu Murai c, Tooru Takahashi c<br><br>b Tohoku Electric Power Co.Inc., Sendai980-8550, Japan<br><br>c Sankyo-Tateyama Aluminum Industry Co. Ltd., Imizu934-8577, Japan<br><br>Received 26 February 2010; revised 11 March 2010; accepted 15 March 2010<br><br># Abstract<br><br>In order to investigate the fatigue properties of extruded magnesium alloy in very high-cycle regime, rotary bending fatigue test was performed in ambient atmosphere at room temperature using the hourglass shaped specimens of AZ80 alloys extruded (F-specimen) and treated by an artificial aging after extrusion (T5-specimen). From the experimental results, both specimens show a clear step-wise S-N curve on which two knees exists. Specific stress amplitude formed the knee corresponded to the 0.2% offset proof stress of 160MPa in compression. From the detailed observation of fracture surface, small facet-like s...</code> |
  | <code>content='1. What experimental method was used to investigate the fatigue properties of extruded AZ80 magnesium alloys in the study?  \n2. How does the crack initiation mechanism change with varying stress amplitudes in the AZ80 magnesium alloys?' additional_kwargs={'refusal': None} response_metadata={'token_usage': {'completion_tokens': 46, 'prompt_tokens': 731, 'total_tokens': 777, 'completion_tokens_details': {'accepted_prediction_tokens': 0, 'audio_tokens': 0, 'reasoning_tokens': 0, 'rejected_prediction_tokens': 0}, 'prompt_tokens_details': {'audio_tokens': 0, 'cached_tokens': 0}}, 'model_name': 'gpt-4o-mini-2024-07-18', 'system_fingerprint': 'fp_7fcd609668', 'finish_reason': 'stop', 'logprobs': None} id='run-5e3c339c-30e6-4dc7-bacb-24b9143312ad-0' usage_metadata={'input_tokens': 731, 'output_tokens': 46, 'total_tokens': 777, 'input_token_details': {'audio': 0, 'cache_read': 0}, 'output_token_details': {'audio': 0, 'reasoning': 0}}</code> | <code># Fatigue behaviour and fractography of extruded AZ80 magnesium alloys in very high cycle regime<br><br># Kazuaki Shiozawaa *, Tomoki Kashiwagi b, Tutomu Murai c, Tooru Takahashi c<br><br>b Tohoku Electric Power Co.Inc., Sendai980-8550, Japan<br><br>c Sankyo-Tateyama Aluminum Industry Co. Ltd., Imizu934-8577, Japan<br><br>Received 26 February 2010; revised 11 March 2010; accepted 15 March 2010<br><br># Abstract<br><br>In order to investigate the fatigue properties of extruded magnesium alloy in very high-cycle regime, rotary bending fatigue test was performed in ambient atmosphere at room temperature using the hourglass shaped specimens of AZ80 alloys extruded (F-specimen) and treated by an artificial aging after extrusion (T5-specimen). From the experimental results, both specimens show a clear step-wise S-N curve on which two knees exists. Specific stress amplitude formed the knee corresponded to the 0.2% offset proof stress of 160MPa in compression. From the detailed observation of fracture surface, small facet-like s...</code> |
  | <code>content='1. What is the chemical composition of the AZ80 magnesium alloy used in the study?\n2. How was the T5 treatment applied to the specimens, and what was its purpose in the experiment?' additional_kwargs={'refusal': None} response_metadata={'token_usage': {'completion_tokens': 41, 'prompt_tokens': 617, 'total_tokens': 658, 'completion_tokens_details': {'accepted_prediction_tokens': 0, 'audio_tokens': 0, 'reasoning_tokens': 0, 'rejected_prediction_tokens': 0}, 'prompt_tokens_details': {'audio_tokens': 0, 'cached_tokens': 0}}, 'model_name': 'gpt-4o-mini-2024-07-18', 'system_fingerprint': 'fp_7fcd609668', 'finish_reason': 'stop', 'logprobs': None} id='run-1ea8b034-255f-4994-b459-394267605838-0' usage_metadata={'input_tokens': 617, 'output_tokens': 41, 'total_tokens': 658, 'input_token_details': {'audio': 0, 'cache_read': 0}, 'output_token_details': {'audio': 0, 'reasoning': 0}}</code>                                                        | <code># 2. Experimental Procedures<br><br># 2.1. Testing materials and specimen<br><br>The material used in this study was commercial Mg-Al-Zn magnesium alloy, AZ80. The chemical composition of these materials (in mass percentage) is 8.24Al, 0.67Zn, 0.20Mn, 0.005Fe, 0.012Si, 0.0008Cu, 0.0007Ni and balanced Mg. The bar with 16mm in diameter was extruded from a billet of 160mm diameter (an extrusion ratio of 99.4:1) under the extrusion ram speed of 1.5m/min at temperature of 623K. Hour-glass shaped specimens with a grip diameter of 10 mm and minimum diameter of 5 mm (Fig. 1) was machined from the extruded bar with the loading axis parallel to their extrusion directions. The elastic stress concentration factor, Kt, of these specimens was 1.065. On the other hand, to investigate the effect of an aging treatment on fatigue behavior, specimens were prepared from the extruded bar which was heated at 473K for 32h and then air-cooled (T5 treatment). From now on, the specimen extruded and no heat-treated is refer...</code>                         |
* Loss: [<code>MatryoshkaLoss</code>](https://sbert.net/docs/package_reference/sentence_transformer/losses.html#matryoshkaloss) with these parameters:
  ```json
  {
      "loss": "MultipleNegativesRankingLoss",
      "matryoshka_dims": [
          768,
          512,
          256,
          128,
          64
      ],
      "matryoshka_weights": [
          1,
          1,
          1,
          1,
          1
      ],
      "n_dims_per_step": -1
  }
  ```

### Training Hyperparameters
#### Non-Default Hyperparameters

- `eval_strategy`: steps
- `per_device_train_batch_size`: 16
- `per_device_eval_batch_size`: 16
- `num_train_epochs`: 25
- `multi_dataset_batch_sampler`: round_robin

#### All Hyperparameters
<details><summary>Click to expand</summary>

- `overwrite_output_dir`: False
- `do_predict`: False
- `eval_strategy`: steps
- `prediction_loss_only`: True
- `per_device_train_batch_size`: 16
- `per_device_eval_batch_size`: 16
- `per_gpu_train_batch_size`: None
- `per_gpu_eval_batch_size`: None
- `gradient_accumulation_steps`: 1
- `eval_accumulation_steps`: None
- `torch_empty_cache_steps`: None
- `learning_rate`: 5e-05
- `weight_decay`: 0.0
- `adam_beta1`: 0.9
- `adam_beta2`: 0.999
- `adam_epsilon`: 1e-08
- `max_grad_norm`: 1
- `num_train_epochs`: 25
- `max_steps`: -1
- `lr_scheduler_type`: linear
- `lr_scheduler_kwargs`: {}
- `warmup_ratio`: 0.0
- `warmup_steps`: 0
- `log_level`: passive
- `log_level_replica`: warning
- `log_on_each_node`: True
- `logging_nan_inf_filter`: True
- `save_safetensors`: True
- `save_on_each_node`: False
- `save_only_model`: False
- `restore_callback_states_from_checkpoint`: False
- `no_cuda`: False
- `use_cpu`: False
- `use_mps_device`: False
- `seed`: 42
- `data_seed`: None
- `jit_mode_eval`: False
- `use_ipex`: False
- `bf16`: False
- `fp16`: False
- `fp16_opt_level`: O1
- `half_precision_backend`: auto
- `bf16_full_eval`: False
- `fp16_full_eval`: False
- `tf32`: None
- `local_rank`: 0
- `ddp_backend`: None
- `tpu_num_cores`: None
- `tpu_metrics_debug`: False
- `debug`: []
- `dataloader_drop_last`: False
- `dataloader_num_workers`: 0
- `dataloader_prefetch_factor`: None
- `past_index`: -1
- `disable_tqdm`: False
- `remove_unused_columns`: True
- `label_names`: None
- `load_best_model_at_end`: False
- `ignore_data_skip`: False
- `fsdp`: []
- `fsdp_min_num_params`: 0
- `fsdp_config`: {'min_num_params': 0, 'xla': False, 'xla_fsdp_v2': False, 'xla_fsdp_grad_ckpt': False}
- `fsdp_transformer_layer_cls_to_wrap`: None
- `accelerator_config`: {'split_batches': False, 'dispatch_batches': None, 'even_batches': True, 'use_seedable_sampler': True, 'non_blocking': False, 'gradient_accumulation_kwargs': None}
- `deepspeed`: None
- `label_smoothing_factor`: 0.0
- `optim`: adamw_torch
- `optim_args`: None
- `adafactor`: False
- `group_by_length`: False
- `length_column_name`: length
- `ddp_find_unused_parameters`: None
- `ddp_bucket_cap_mb`: None
- `ddp_broadcast_buffers`: False
- `dataloader_pin_memory`: True
- `dataloader_persistent_workers`: False
- `skip_memory_metrics`: True
- `use_legacy_prediction_loop`: False
- `push_to_hub`: False
- `resume_from_checkpoint`: None
- `hub_model_id`: None
- `hub_strategy`: every_save
- `hub_private_repo`: None
- `hub_always_push`: False
- `gradient_checkpointing`: False
- `gradient_checkpointing_kwargs`: None
- `include_inputs_for_metrics`: False
- `include_for_metrics`: []
- `eval_do_concat_batches`: True
- `fp16_backend`: auto
- `push_to_hub_model_id`: None
- `push_to_hub_organization`: None
- `mp_parameters`: 
- `auto_find_batch_size`: False
- `full_determinism`: False
- `torchdynamo`: None
- `ray_scope`: last
- `ddp_timeout`: 1800
- `torch_compile`: False
- `torch_compile_backend`: None
- `torch_compile_mode`: None
- `dispatch_batches`: None
- `split_batches`: None
- `include_tokens_per_second`: False
- `include_num_input_tokens_seen`: False
- `neftune_noise_alpha`: None
- `optim_target_modules`: None
- `batch_eval_metrics`: False
- `eval_on_start`: False
- `use_liger_kernel`: False
- `eval_use_gather_object`: False
- `average_tokens_across_devices`: False
- `prompts`: None
- `batch_sampler`: batch_sampler
- `multi_dataset_batch_sampler`: round_robin

</details>

### Training Logs
| Epoch   | Step | Training Loss | cosine_ndcg@10 |
|:-------:|:----:|:-------------:|:--------------:|
| 0.8929  | 50   | -             | 0.9525         |
| 1.0     | 56   | -             | 0.9638         |
| 1.7857  | 100  | -             | 0.9801         |
| 2.0     | 112  | -             | 0.9743         |
| 2.6786  | 150  | -             | 0.9849         |
| 3.0     | 168  | -             | 0.9812         |
| 3.5714  | 200  | -             | 0.9868         |
| 4.0     | 224  | -             | 0.9962         |
| 4.4643  | 250  | -             | 0.9925         |
| 5.0     | 280  | -             | 0.9944         |
| 5.3571  | 300  | -             | 0.9944         |
| 6.0     | 336  | -             | 0.9944         |
| 6.25    | 350  | -             | 0.9944         |
| 7.0     | 392  | -             | 0.9981         |
| 7.1429  | 400  | -             | 0.9962         |
| 8.0     | 448  | -             | 0.9981         |
| 8.0357  | 450  | -             | 0.9981         |
| 8.9286  | 500  | 0.3646        | 0.9981         |
| 9.0     | 504  | -             | 0.9981         |
| 9.8214  | 550  | -             | 0.9981         |
| 10.0    | 560  | -             | 0.9981         |
| 10.7143 | 600  | -             | 0.9981         |
| 11.0    | 616  | -             | 0.9981         |
| 11.6071 | 650  | -             | 0.9981         |
| 12.0    | 672  | -             | 0.9944         |
| 12.5    | 700  | -             | 0.9981         |
| 13.0    | 728  | -             | 0.9981         |
| 13.3929 | 750  | -             | 0.9981         |
| 14.0    | 784  | -             | 0.9981         |
| 14.2857 | 800  | -             | 0.9981         |
| 15.0    | 840  | -             | 0.9981         |
| 15.1786 | 850  | -             | 0.9981         |
| 16.0    | 896  | -             | 0.9981         |
| 16.0714 | 900  | -             | 0.9981         |
| 16.9643 | 950  | -             | 0.9981         |
| 17.0    | 952  | -             | 0.9981         |
| 17.8571 | 1000 | 0.064         | 0.9981         |
| 18.0    | 1008 | -             | 0.9981         |
| 18.75   | 1050 | -             | 0.9981         |
| 19.0    | 1064 | -             | 0.9981         |
| 19.6429 | 1100 | -             | 0.9981         |
| 20.0    | 1120 | -             | 0.9981         |
| 20.5357 | 1150 | -             | 0.9981         |
| 21.0    | 1176 | -             | 0.9981         |
| 21.4286 | 1200 | -             | 0.9981         |
| 22.0    | 1232 | -             | 0.9981         |
| 22.3214 | 1250 | -             | 0.9981         |
| 23.0    | 1288 | -             | 0.9981         |
| 23.2143 | 1300 | -             | 0.9981         |
| 24.0    | 1344 | -             | 0.9981         |
| 24.1071 | 1350 | -             | 0.9981         |
| 25.0    | 1400 | -             | 0.9981         |


### Framework Versions
- Python: 3.11.11
- Sentence Transformers: 3.4.1
- Transformers: 4.48.3
- PyTorch: 2.5.1+cu124
- Accelerate: 1.3.0
- Datasets: 3.3.2
- Tokenizers: 0.21.0

## Citation

### BibTeX

#### Sentence Transformers
```bibtex
@inproceedings{reimers-2019-sentence-bert,
    title = "Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks",
    author = "Reimers, Nils and Gurevych, Iryna",
    booktitle = "Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing",
    month = "11",
    year = "2019",
    publisher = "Association for Computational Linguistics",
    url = "https://arxiv.org/abs/1908.10084",
}
```

#### MatryoshkaLoss
```bibtex
@misc{kusupati2024matryoshka,
    title={Matryoshka Representation Learning},
    author={Aditya Kusupati and Gantavya Bhatt and Aniket Rege and Matthew Wallingford and Aditya Sinha and Vivek Ramanujan and William Howard-Snyder and Kaifeng Chen and Sham Kakade and Prateek Jain and Ali Farhadi},
    year={2024},
    eprint={2205.13147},
    archivePrefix={arXiv},
    primaryClass={cs.LG}
}
```

#### MultipleNegativesRankingLoss
```bibtex
@misc{henderson2017efficient,
    title={Efficient Natural Language Response Suggestion for Smart Reply},
    author={Matthew Henderson and Rami Al-Rfou and Brian Strope and Yun-hsuan Sung and Laszlo Lukacs and Ruiqi Guo and Sanjiv Kumar and Balint Miklos and Ray Kurzweil},
    year={2017},
    eprint={1705.00652},
    archivePrefix={arXiv},
    primaryClass={cs.CL}
}
```

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