Distortional Model Research Articles

Direct application of elasto-visco-plastic self-consistent crystal plasticity model to U-draw bending and springback of dual-phase high strength steel

The incremental elasto-visco-plastic self-consistent polycrystal model (ΔEVPSC) was utilized to describe the constitutive behavior of dual-phase 980 (DP980) steel. A simple baseline modeling approach was chosen: the hardening behavior of each constituent phase in the DP980 steel was described by a simple Voce hardening law without explicitly considering the back stress; and it was assumed that using the same single crystal elastic modulus for ferrite and martensite is sufficiently representative. The adequacy of this baseline modeling approach was evaluated by comparing various mechanical experimental data with model predictions in terms of the stress vs. strain curves obtained from uniaxial tension, tension-compression, and loading-unloading-loading (LUL) tests. Additionally, the evolution of experimental lattice strain data reported in literature was used to validate the phase-specific Voce hardening parameters. Despite its minimalistic modeling description, the baseline ΔEVPSC model successfully captured key features: 1) the Bauschinger effect, 2) the decrease in chord modulus, and 3) the non-linearity in the stress vs. strain curves resulting from the LUL test. All three mentioned characteristics are crucial for accurate prediction of springback in sheet metals. The ΔEVPSC model, interfaced with a finite element solver (Abaqus/standard) as the user material subroutine, was employed to simulate the Numisheet93 benchmark problem. The strip of DP980 was first U-drawn followed by springback. The model-predicted springback profile aligned well with the experimental results only when stress relaxation was properly considered, resulting in improved predictive accuracy compared to predictions based on a distortional plasticity model.

User friendly FE Formulation for anisotropic distortional hardening model based on non-associated flow plasticity and its application to springback prediction

Based on non-associated flow plasticity, a newly developed anisotropic distortional hardening model developed by Hu and Yoon [15] is implemented in finite element analysis in a user-friendly manner. The derivatives of complex hardening models are calculated using the Finite Difference Method (FDM), which is much more convenient than using the analytical derivatives. To further improve the accuracy of the proposed method, the step size analysis in FDM is performed by analyzing the derivative formation. To evaluate the accuracy and computational efficiency of a proposed step size for FDM, single element simulations are performed under different loading paths. It has been found that the maximum absolute error of the flow curves between the simulation and the theoretical result is less than 0.3%. The U-bending tests for DP600 and TRIP1180 are used to verify the ability of the distortional hardening model for springback prediction. The simulation result of the strain hardening model is in good agreement with the experiment. The computational efficiency is also increased by 24% due to the improved convergence rate.

Modeling of distortional hardening including plane strain tension and pure shear for a TWIP steel

This paper focuses on calibrating and modeling of distortional hardening behaviours in twinning induced plasticity steels. True stress-strain curves for uniaxial tension, plane strain tension, and pure shear specimens are inversely identified from corresponding load-displacement curves. The study reveals that accurately predicting the hardening behaviours of TWIP980 steel under plane strain tension and pure shear stress states is challenging with an isotropic hardening model, and a negative hydrostatic effect for TWIP980 is observed through shear testing. A novel distortional hardening model is proposed to simultaneously accommodate the three stress states on the contours of plastic work. Coefficients of the distortional hardening model are calibrated at discrete levels of plastic work and then interpolated to describe the distortion of the initial yield surface. The model is then expanded to consider the true stress-strain curves under uniaxial tension along 0, 45 and 90-degree directions, as well as under the plane strain tension along the 0-degree direction simultaneously. This expansion explicitly incorporates the three true stress-strain curves under uniaxial tension, with the curve of plane strain tension captured by an evolutionary exponent related to plastic work. The developed distortional hardening models demonstrate reasonable reproduction of load-displacement curves for TWIP980 steel under uniaxial tension, plane strain tension, and pure shear stress states.

Characterisation and modelling of anisotropic hardening behaviour of cubic and hexagonal close packed polycrystalline metals

ABSTRACT In this study, anisotropic non-proportional hardening behaviour of the sheet metals with different crystalline structures is investigated. The investigated materials particularly exhibit the Bauschinger effect and complex transient hardening behaviour during loading path change. Furthermore, the finite element simulations are carried out to evaluate the performance of the distortional and multi-surface-kinematic hardening models in flow stress prediction under loading path change. Both models can well reproduce the measured anisotropic hardening, but the distortional hardening concept shows better predictive capability for flow stresses. The improved accuracy of the flow stress prediction with the distortional hardening model compared to the kinematic hardening is attributed to its flexibility in distortion of the yield surface following microstructure deviator independent on the initial yield surface. In contrast, the initial size of the yield surface in the kinematic hardening significantly affects the determination of the re-yielding stress at load reversal.

Application of distortional plasticity framework to EDDQ and TRIP steel sheets: Prediction of latent hardening and its influence on springback

In this study, the recently developed distortional plasticity model (HAH20) was applied to EDDQ and TRIP steel sheets to account for hardening fluctuations induced by loading path changes. Previous non-linear loading path experiments, which were tension-compression, tension-tension, and tension-shear tests, revealed intricate latent hardening in EDDQ steel and a combination of latent hardening and cross loading contraction in TRIP steel. The HAH20 model was calibrated using tension-compression and 90° tension–45° tension tests with adjustment of setting parameters for accurate latent hardening prediction. Then, a comparison between the HAH20 model and the previous distortional plasticity model (HAH14) in the other independent experiments highlights the superiority of HAH20 model due to its description of latent hardening. Furthermore, for TRIP steel, the HAH20 and HAH14 models were applied to predict springback in a U-draw bending test featuring a novel curved blank subjected to reverse and cross loading states simultaneously. The simulation results show that the HAH20 model predicts springback more accurately than the HAH14 model; however, the main reason is the accurate description of reverse loading in the HAH20 model. This is due to the intricate interplay between cross loading contraction and latent hardening in springback.

Appropriateness of hydrostatic pressure-based modeling for strength differential effect in advanced high strength steel

Although numerous models have been proposed to describe the strength differential (SD) effect, their appropriateness and efficiency in the case of advanced high strength steel (AHSSs) have not been investigated. To this end, this study investigates the SD effect in AHSS using a hydrostatic-pressure-dependent plasticity theory. Although pressure model can effectively predict the SD effect in AHSSs with only one coefficient, the original formulation is experimentally inconsistent in the first quadrant of a yield surface. Hence, this study developed a new formulation to remove the inconsistency in a simple manner and validated the pressure model using new experimental data reported for two recently developed AHSSs: DP980 and MART1500Y. The SD effect is characterized based on monotonic compression and tension tests in three different directions with respect to the rolling direction to obtain the stress–strain curves and r-values. Next, the pressure model is used to predict the plastic behavior of both steel sheets. The parallel transition of flow stress and similarity in r-values between the tension and compression states supports the appropriateness of the proposed pressure-based modeling. Furthermore, these insights substantiate the fact that deformation mechanisms cannot explain the SD effect in both steel sheets. Therefore, complex yield functions that describe the SD effect in general materials are not necessary in the case of AHSS. Additionally, the pressure model is incorporated into a distortional plasticity model for applying it to springback in the bending process. The distortional plasticity model with and without the pressure model is calibrated using tension–compression curves, thereby revealing that the SD significantly affects the calibration. Finally, a U-draw bending experiment and the corresponding finite element simulation are conducted to compare the springback; the results show that considering the SD effect improves the springback simulation accuracy.

Non-iterative stress projection method for anisotropic hardening

In this paper, a fully explicit non-iterative stress projection method for the instant stress integration of advanced plasticity models that account for the history-dependent deformation is proposed. In this non-iterative stress projection method, the stress increment is directly determined based on the elastoplastic constitutive law. Generalized formulations of the elastoplastic tangent moduli for anisotropic hardening models are discussed considering the morphological yield surface changes in the context. Precise integrations of the stress tensor, effective plastic strain, and other state variables are accomplished for kinematic- and distortional hardening models. The implemented plasticity hardening models are validated through a series of non-proportional loadings and a sheet metal forming simulation to check the fidelity, numerical robustness, and computational efficiency of the suggested non-iterative stress projection method. Consequently, the computation cost for a large-scale metal forming simulation is reduced up to 50%.

A new simplified distortional hardening model for nonlinear strain paths

The material behaviors under nonlinear strain paths have been successfully explained through distortional hardening model in which the yield surface is mainly rotating and contracting as plastic deformation occurs. In order to apply to industrial applications, it is beneficial for any constitutive model including distortional hardening model to have simplicity of equation, which is related to numerical efficiency, as well as accuracy in describing material behaviors. This study was mainly motivated to construct a simple form of equation for distortional hardening model with reasonable accuracy as the conventional distortional hardening models. In this paper, a new simplified distortional hardening model is proposed by considering one of the pioneering works for distortional hardening (Tozawa, 1978) and definition of homogeneous function. Any yield function could be used for initial anisotropy and asymmetry yielding. In addition, with the combination of isotropic hardening model for consistency condition, the new model could explain both isotropic and anisotropic hardening under proportional and non-proportional loading paths. The proposed model reasonably described the material behaviors including Basuchinger effect, permanent softening, nonlinear transient behavior, and yield surface contraction. Finally, the availability in finite element simulation has been identified from the springback prediction in U-draw bending.

Efficient and robust stress integration algorithm for anisotropic distortional hardening law under cross-loading with latent hardening

A fast and robust stress-update algorithm based on the general cutting-plane method (GCPM) was developed for a distortional hardening model, known as the HAH-DPS model. It captures the anisotropic hardening behaviors such as the Bauschinger effect, transient hardening, differential permanent softening, and cross-loading effects. The lower computational efficiency of the direct application of GCPM was rectified by considering the all-evolutionary plastic state variables during iterations. The newly proposed algorithm was formulated on the dependence of the equivalent plastic strain and the other state variables defined in the distortional hardening model. And it was implemented in a commercial finite element software using a user-defined material subroutine (UMAT). Finite element simulations under strain-path change were carried out to demonstrate the performance of the new numerical algorithm in terms of the convergence behavior locally as well as globally.

Characterization of kinematic and distortional hardening by cyclic twin-bridge shear tests for sheet metal with inverse engineering approach

This study characterizes the plastic behavior under cyclic loading for an aluminum alloy of 5182-O and advanced high strength steel of QP1180. Twin-bridge shear specimens were loaded cyclically to evaluate the reverse shear loading behavior of the tested materials with different pre-strain from small (0.05 major strain) to large (0.15). The plastic behavior under cyclic loading is modelled by kinematic and distortional hardening models under the non-associated flow rule (NAFR) by anisotropic Drucker (Aniso-Drucker) yield function. An additional shear constraint proposed by (Abedini et al., 2018) is imposed on the plastic potential of NAFR. The Zang and HAH20 models are selected as kinematic and distortional hardening models respectively. They are calibrated inversely by the reverse torque-torsion angle curves from experiments. Finally, V-bending tests with the pre-strained strips were carried out and simulated by the calibrated hardening model to evaluate its predicting accuracy. The results show that twin-bridge shear test combined with the recommended inverse engineering approach is implementable to overcome the drawback of the simple shear test due to inhomogeneous deformation in large strain. The constitutive models are critical for the inverse calibration. It is found that the calibration accuracy under NAFR is higher than the associated flow rule (AFR) especially for large strain conditions. Also, the additional shear constraint imposed on the plastic potential of NAFR is found to be an effective approach to enforce the simulated shear stress at zero hydrostatic pressure. As for hardening model, the HAH model has more flexibility compared to the kinematic hardening model benefiting from its distortional hardening form. Also, parameters related to permanent softening in the new HAH20 model need to be evaluated carefully at the large deformations.

Experimental characterization and modeling of complex anisotropic hardening in quenching and partitioning (Q&P) steel subject to biaxial non-proportional loadings

Quenching and partitioning (Q&P) steels, as one of the third-generation advanced high strength steels, exhibit complex anisotropic hardening behavior under biaxial non-proportional loadings. In this study, a wide range of strain path changes (SPCs) defined as an angle (χ) between stress deviators before and after the SPC is experimentally applied to characterize the anisotropic hardening of a Q&P steel with a strength grade of 980 MPa (QP980). The investigated SPCs include uniaxial tension followed by compression (UT-UC; χ=180°), uniaxial compression followed by tension (UC-UT; χ=180°), uniaxial tension followed by plane strain (UT-PS; χ=30°), equi-biaxial tension followed by plane strain (EBT-PS; χ=30°), followed by uniaxial tension (EBT-UT; χ=60°) and followed by simple shear (EBT-SH; χ=90°). These SPCs are achieved by the program-controlled biaxial tensile testing equipment using novel arm-reinforced cruciforms. The experimental findings in the QP980 steel sheet are summarized as follows: (1) Strong strain-dependent Bauschinger effect, transient hardening and permanent softening are observed in both UT-UC and UC-UT loadings; (2) Bauschinger effect increases as strain increases, and it exhibits obvious tension-compression asymmetry; (3) The transient hardening behaviors are path-dependent under SPCs with various χ; (4) The Bauschinger coefficient is approximately a parabola function of cosχ; (5) The most significant strength softening occurs under EBT-SH loading. In order to describe the complex hardening behavior of the QP980 steel, a distortional hardening model is proposed on the basis of non-associated flow rule. A coupled quadratic and stress-invariant-based yield function is used to describe stress anisotropy, strength differential effect, and anisotropic hardening for proportional loadings. Then, the Bauschinger effect related hardening and path-dependent permanent softening are captured by a modified homogeneous anisotropic hardening model. The calibrated model parameters and experimental validations demonstrate that the strain- and path-dependent Bauschinger effect can be well predicted by the proposed constitutive model. Especially, the model enables to accurately describe both the asymmetric anisotropic hardening and yield surface distortions of the QP980 steel at various biaxial SPCs.

Finite element implementation of hydrostatic pressure-sensitive plasticity and its application to distortional hardening model and sheet metal forming simulations

• The strength-differential (SD) effect of AHSS with ultimate tensile strength exceeding 1 GPa is modeled by a hydrostatic pressure-dependent distortional plasticity theory. • The finite element implementation of the pressure-dependent plasticity theory is proposed in the manuscript. The implemented theory is validated with the comparison study with the associated stand-alone code and experimental measurements. • Both the SD- and strain patch change effects of TIRP1180 are reproduced in finite element simulation by embedding the distortional plasticity model, HAH 20 , in the pressure-dependent yield condition. The effectiveness and applicability of the FE-implemented pressure-dependent distortional plasticity model in sheet metal forming simulations is validated through the springback prediction studies. In this work, the hydrostatic pressure-dependency of the distortional plasticity model HAH 20 was implemented using a finite element (FE) code to account for the strength-differential (SD) effect that has been observed in advanced high-strength steel sheets. To this end, a fully-implicit stress update algorithm formulation was introduced for the pressure-dependent plasticity theory. The implementation was validated by comparing the FE prediction of the material behavior during a number of tests with those of a stand-alone code of the constitutive description as well as with experimental data. In order to investigate the SD effect on the springback simulation results, the U-draw bending test was analyzed within this FE framework. Furthermore, in order to assess the effectiveness and stability of the formulation for a large-scale example, forming simulations of an automotive structural part were conducted. In addition to the SD effect, strain path changes and geometrical aspects were also investigated in this example. It was shown that the distortional plasticity-based pressure-dependent yield criterion well describes the asymmetric SD behavior in sheet metal forming simulations.

Fully Implicit Stress Update Algorithm for Distortion-Based Anisotropic Hardening with Cross-Loading Effect: Comparative Algorithmic Study and Application to Large-Size Forming Problem

A fully implicit stress integration algorithm is developed for the distortional hardening model, namely the e−HAH model, capable of simulating cross−hardening/softening under orthogonal loading path changes. The implicit algorithm solves a complete set of residuals as nonlinear functions of stress, a microstructure deviator, and plastic state variables of the constitutive model, and provides a consistent tangent modulus. The number of residuals is set to be 20 or 14 for the continuum or shell elements, respectively. Comprehensive comparison programs are presented regarding the predictive accuracy and stability with different numerical algorithms, strain increments, material properties, and loading conditions. The flow stress and r−value evolutions under reverse/cross−loading conditions prove that the algorithm is robust and accurate, even with large strain increments. By contrast, the cutting−plane method and partially implicit Euler backward method, which are characterized by a reduced number of residuals, result in unstable responses under abrupt loading path changes. Finally, the algorithm is implemented into the finite element modeling of large−size, S−rail forming and the springback for two automotive steel sheets, which is often solved by a hybrid dynamic explicit–implicit scheme. The fully implicit algorithm performs well for the whole simulation with the solely static implicit scheme.

Prediction of anisotropic strengths of steel plate after prior bending-reverse bending deformation: Application of distortional hardening model

In this study, the strengths of a steel pipe in different material orientations are predicted using a distortional anisotropic hardening model, namely, the HAH model, implemented in a finite element simulation. The investigated hardening can capture the transient flow behavior under bending and reverse bending strain paths. In addition, the model reproduces the material behavior under orthogonally applied tension from the prior deformation path. To improve the predictive accuracy of the existing distortional hardening model, we additionally implement the multi-component evolution rule of the Bauschinger effect and transient hardening behavior. Two-step tension tests are used to identify the constitutive parameters related to the loading path changes in the bending and reverse bending (BRB) test, which mimics the common pipe manufacturing process in a practical manner. The predicted strengths along the circumferential and transverse directions to the major bending direction agree well with the experimentally measured strengths when the distortional hardening model is employed. By contrast, the classical isotropic hardening and kinematic hardening model over- and under-estimate the yield strength of the specimens after prior BRB loading. The improved accuracy of the strength prediction with the investigated HAH is attributed to the anisotropic identification of the flow behavior under both load reversal and cross-loading conditions, whereas the isotropic-kinematic hardening only considers the back stress evolution at load reversal. In addition to the strengths, the stagnated flow behavior after BRB loading can be well predicted with the HAH model with a properly calibrated yield point elongation using an inverse identification method.

A distortional hardening model for finite plasticity

Plastic anisotropy may strongly affect the stress and strain response in metals subjected to multiaxial cyclic loading. This anisotropy evolves due to various microstructural features. We first use simple models to study how such features result in evolving plastic anisotropy. A subsequent analysis of existing distortional hardening models highlights the difference between stress- and strain-driven models. Following this analysis, we conclude that the stress-driven approach is most suitable and propose an improved stress-driven model. It is thermodynamically consistent and guarantees yield surface convexity. Many distortional hardening models in the literature do not fulfill the latter. In contrast, the model proposed in this work has a convex yield surface independent of its parameter values. Experimental results, considering yield surface evolution after large shear strains, are used to assess the model’s performance. We carefully analyze the experiments in the finite strain setting, showing how the numerical results can be compared with the experimental results. The new model fits the experimental results significantly better than its predecessor without introducing additional material parameters.

Modeling differential permanent softening under strain-path changes in sheet metals using a modified distortional hardening model

In this study, a modified distortional hardening model is proposed based on the homogeneous yield-function based anisotropic hardening (HAH). An improvement is made to capture differential permanent softening (DPS) under strain-path changes in sheet metals, whereas the other anisotropic hardening features such as the Bauschinger effect, transient behavior, and cross hardening phenomenon are retained as they are in the original HAH model.The modified HAH (M-HAH) model is implemented in a commercial finite element software using the user-defined material subroutine, and validated well by reproducing the flow stress behaviors after differently programmed strain-path changes for dual-phase steel, extra deep drawing quality steel, and ferritic stainless steel. Additionally, the M-HAH can simulate the DPS in two-step tension tests, which cannot be accurately modeled by the original HAH. Finally, the V-bending springback tests with pre-tensioned specimens are evaluated with different modeling schemes including the classical isotropic hardening, kinematic hardening and distortional hardening models.

Experimental and theoretical plasticity analyses of steel materials deformed under a nonlinear strain path

In this study, the macroscopic mechanical behavior of extra-deep drawing quality (EDDQ) and transformation-induced plasticity (TRIP1180) steels subjected to nonlinear-strain-path modes of deformation was investigated. For the nonlinear-strain-path experiments conducted on steels, an optimized experimental approach was proposed for deforming the material using two linear loading segments with a single abrupt change in the strain path. A specific medium-scale uniaxial tension specimen was designed for the pre-strain stage. The advantage of this approach over existing methods was that it enabled testing of various strain-path changes for steels with strengths greater than 1 GPa within a reasonable load range. In addition, this approach produced a more uniform strain field, which is important during the pre-strain stage. After the uniaxial pre-strain, various specimens were extracted from the uniformly deformed area for use in experiments involving changes in the strain path. To predict the material behavior under nonproportional loading, the homogeneous anisotropic hardening (HAH) distortional plasticity model was selected. The predictions of the HAH model were compared with the corresponding experimental results to assess the suitability of the constitutive model to accurately reproduce the observed effects of strain-path changes.

Validation of homogeneous anisotropic hardening model using non-linear strain path experiments

We conducted non-linear strain path experiments on a dual-phase steel-sheet sample. The first strain path in each of these experiments, called pre-strain, was always uniaxial tension in the direction transverse to the sheet (90° from the rolling direction). For this purpose, we clamped large tensile specimens in a suitable gripping system and deformed them to produce a sufficiently large area with a uniform strain distribution. We machined new specimens from this area, and we subjected them to different modes of deformation, namely uniaxial tension in different directions from the transverse direction, simple shear, and biaxial tension with different load ratios. In addition, we performed uniaxial tension-compression tests consisting of either one or three full cycles. We obtained the coefficients of a distortional plasticity model—the homogeneous anisotropic hardening (HAH) model—using an inverse analytical identification tool. First, we calibrated two sets of reverse loading coefficients using the tension-compression stress–strain curves obtained with either one or three full cycles. Then we used the 90° tension–45° tension and the 90° tension–0° simple-shear sequences to determine two sets of cross-loading coefficients. We compared the other independent experimental flow curves with simulations using the HAH model with combinations of the different sets of coefficients. These comparisons showed the influence of the selected input data on the calculations of the coefficients calibrated and demonstrated the advantages and limitations of the present HAH model.

Investigation of Anisotropic Subsequent Yield Behavior for 45 Steel by the Distortional Yield Surface Constitutive Model.

The subsequent anisotropic yield behavior of 45 steel was predicted by the distortional yield surface constitutive model, which can describe the anisotropic subsequent yield and the cross effect of metal associating with loading history. The yield characteristics and plastic hardening behaviors of the 45 steel were simulated under three preloading paths including pre-torsion, pre-tension, and pre-tension–torsion. Based on the comparison between the experimental yield stresses and the simulation by the classical Chaboche model, the proposed model can describe the remarkable anisotropic yield behavior related to the loading history, which can effectively describe the sharp point of yield surface in pre-loading direction and the smaller curvature near its opposite direction. It was successfully simulated by the constitutive model proposed that the subsequent distortional yield surface defined by small offset strain and the degradation process of the distortion feature defined by large offset strain.

Determination of Modelling Error Statistics for Cold‐Formed Steel Columns

In this article, an attempt has been made to estimate the Modelling Error (ME) associated with compression capacity models available in international standards for different failure modes of compression members fabricated from Cold‐Formed Steel (CFS) lipped channel sections. For the first time, a database has been created using test results available in the literature for compression capacities of CFS lipped‐channel sections. The database contains details of 273 numbers of compression member tests which have failed in different failure modes, namely, (i) flexural, torsional, flexural‐torsional, local, and distortion buckling and (ii) failure by yielding. Only those sources, which report all the details, required to compute the capacities using different standards are included in the database. The results of experimental investigations carried out at CSIR‐Structural Engineering Research Centre, Chennai, are also included in this test database. The international codes of practice used in calculation of compression capacities of the database columns considered in this paper are ASCE 10‐15 (2015), AISI S100‐16 (2016), AS/NZS 4600: 2018 (2018), and EN 1993‐1‐3:2006 (2006). The ASCE, AISI, AS/NZS, and EN design standards have different design guidelines with respect to the failure modes, e.g., ASCE 10‐15 (2015) standard provides stringent criteria for maximum width to thickness ratio for stiffened and unstiffened elements. Hence, guidelines for the distortional buckling mode are not provided, whereas the AISI S100‐16 (2016) and AS/NZS 4600: 2018 (2018) standards consider separate guidelines for distortional buckling mode and EN 1993‐1‐3:2006 (2006) standard considers combined local and distortional buckling mode. Further, the sample size for each design standard is varying depending on the design criteria and failure mode. Studies on statistical analysis of ME suggest that the compression capacity predicting models for flexural‐torsional buckling mode are associated with large variation irrespective of the design standard. Similar observations are made for the flexural buckling model as per EN 1993‐1‐3:2006 (2018) standard and distortional buckling models as per AISI S100‐16 (2016) and AS/NZS 4600: 2018 (2018) standards. The compression capacities for test database sections are evaluated by neglecting the partial safety factors available in design standards. The probabilistic analysis to determine statistical characteristics of compression capacity indicates the importance of consideration of ME as a random variable. Hence, the ME results will be useful in code calibration studies and may have potential reference to design practice.