The strain compensation method for measuring in-plane forming limit curves (FLCs) using 2D digital image correlation developed previously [A method of measuring in-plane forming limit curves using 2D Digital Image Correlation, SAE Int. J. Mater. Manf., 2023] was modified and extended to more versatile and popular out-of-plane FLCs. The current study introduces a straightforward strain compensation technique for measuring Nakazima testing based out-of-plane FLCs utilizing an affordable single-camera (2D) DIC system. In this study, forming tests are performed on two automotive-grade sheet metal alloys: DP980 steel and a 6xxx series aluminum alloy using the Nakazima test method. The experiments are conducted on a customized setup that allows for simultaneous optical strain measurements using both a stereo DIC and a 2D DIC system. The FLCs are obtained by applying a temporal FLC computation approach to the two measurement sets. The results show that 2D DIC FLC points match those obtained by stereo DIC for both the materials after applying the proposed strain correction method.

With the introduction of advanced lightweight materials with complex microstructures and behaviors, more focus is put on the accurate determination of their forming limits, and that can only be possible through experiments as the conventional theoretical models for the forming limit curve (FLC) prediction fail to perform. Despite that, CAE engineers, designers, and toolmakers still rely heavily on theoretical models due to the steep costs associated with formability testing, including mechanical setup, a large number of tests, and the cost of a stereo digital image correlation (DIC) system. The international standard ISO 12004-2:2021 recommends using a stereo DIC system for formability testing since two-dimensional (2D) DIC systems are considered incapable of producing reliable strains due to errors associated with out-of-plane motion and deformation. This work challenges that notion and proposes a simple strain compensation method for the determination of FLCs using a low-cost single-camera (2D) DIC system. In this study, formability tests are performed on an automotive-grade 6xxx series aluminum alloy using the Marciniak in-plane FLC testing method. The tests are performed on a custom setup that enables simultaneous optical strain measurements using a stereo DIC as well as a 2D DIC system. The results show how 2D DIC FLC points match those obtained by stereo DIC using two popular FLC approaches: ISO 12004-2 section-based spatial method and a time-dependent linear best fit (LBF) method.

One of the main challenges in the joining of multi-material components is the assessment of the nature and magnitude of the residual stresses developing in the adhesive bond during the heat curing manufacturing process. Numerical modeling of these residual stresses can provide insights for making informed decisions related to (i) material substrate properties; (ii) adhesive properties i.e., low, medium, or high stiffness; (iii) bondline geometry i.e., bondline width and bead thickness; (iv) curing cycle characteristics; and (v) fixation design i.e., type, spacing, the number of joints. This work presents a cure history-dependent viscoelastic-plastic material description for the modeling of adhesive bonded joints. The main highlight of the work is the multi-physics modeling package consisting of a curing kinetics model, a cure-dependent viscoelastic model, and a temperature, strain-rate dependent plastic model formulation which can be coded in any finite element solver. The modeling approach can predict the residual stresses in the adhesive bond due to the accumulated viscoelastic as well as plastic strains occurring during the heat curing process. For the purpose of validation, the model is coded into a user-defined material subroutine (UMAT) in LS-DYNA. The modeling approach is verified at a small specimen level by simulating a uniaxial tension specimen at various temperatures and strain rates. The performance of the modeling approach is further evaluated at the component level using specially designed experiments involving heat curing of a sub-sized multi-material automotive roof model. The thermal displacements and distortions in the roof structure captured using 3D digital image correlation are compared to the finite element model predictions. Several design guidelines related to adhesive selection and mechanical fixations are proposed as a result of the study.

In sheet metal forming and stamping operations, modeling the behavior of sheet metal alloys for springback prediction is known to be very challenging, not only because of the complex models needed to account for kinematic hardening (such as the Yoshida-Uemori Model) but more importantly because of the experimental limitations of our ability to perform the complex tests needed to calibrate such models. For instance, reliable monotonic uniaxial compression tests and then cyclic tension-followed-by-compression tests are essential for characterizing the response of the material under those loading conditions, providing quantitative evaluation of the Bauschinger effect and tension-compression asymmetry in the material, and ultimately generating the right data to calibrate the constitutive model. This work tries to shed some light on this topic by introducing a new antibuckling device that is particularly designed to enable accurate and repeatable compression and cyclic testing. The device exerts side loading on the sheet test sample to prevent it from buckling during testing under compression loading conditions. The device is designed to address the limitations of other approaches and devices presented in the literature, and it features control and monitoring of side forces, self-centering, and the ability to achieve large plastic compressive strains. More importantly, digital image correlation (DIC) is integrated with the antibuckling device and testing load frame to provide accurate strain measurements. In this study, DIC was used in a real-time mode (unlike the typical postdeformation mode) to facilitate accurate load reversal during cyclic testing. For validation, the presented setup was used for testing two selected materials with practical applications in the automotive body sector: AA6016-T4 and DP980 steel sheets. The results demonstrate how the developed setup and the integration with real-time DIC provide a robust and reliable means for generating high-quality curves for the different tests needed for the calibration of springback models.

The rapidly increasing use of thin membranes; especially in the fabrication of flexible electronics, has motivated investigating the wrinkling behavior of these membranes. Wrinkling has an undesirable effect since wrinkles degrade the surface accuracy of structures incorporating thin membranes. This work introduces and evaluates an approach based on including optimized geometric features in thin membranes to suppress their wrinkling behavior. The ability of the optimized geometric features to suppress wrinkling in a 25 μm thick polyimide membrane subjected to uniaxial stretching is investigated computationally and experimentally in this work. A finite element model is developed to predict the wrinkling behavior of the membrane. An experimental setup equipped with 3D digital image correlation system is used to determine the wrinkles pattern, amplitude, and wavelength. Symmetric circular holes are introduced in the membrane to redistribute the stress field, eliminate the fluctuation in the minor principal stress in the membrane, and suppress wrinkles. The location and size of the circular holes are determined by coupling the Non-Linear Programming by Quadratic Largrangian technique and finite element simulations. An optimal design is obtained and the experimental results show that the optimally designed holes effectively suppressed the wrinkling behavior.

The rapidly increasing use of structural adhesives, especially in the joining of automotive body structures has motivated various investigations of the effects of adhesive curing process on joints. The automotive-grade structural adhesives require heat curing, which, in the meantime, performs thermal loading on the substrates and causes undesirable effects in the joint. For example, the curing process results in complex residual stresses in the adhesive bond which are detrimental to the performance of the adhesive bond and thereby the automobile body structure, particularly the crashworthiness. To thoroughly evaluate such effects, this paper consists of two parts. The first part presents an innovative experimental method to characterize the thermal effects of the heat curing process on a multi-material single lap shear joint using digital image correlation. The second part of the study compares the performance of residual stress-induced joints against stress-free joints under tension loading at different strain rates. The proposed experimental method and the corresponding results from this study are expected to help comprehensively understand the adhesive joining process and its potential side effects on the automobile body structure.

The thermal loading during the curing process of an adhesive-bonded joint induces residual stresses in the joint, thereby affecting its performance. The problem becomes worse in the case of a multi-material joint involving varying coefficients of thermal expansion (CTE) for different parts. A novel approach was developed to model the properties of automotive grade structural adhesives during the heat curing process. The material model was divided into two components: curing kinetics model and viscoelastic mechanical model. The models were calibrated using experimental data from Differential Scanning Calorimetry (DSC) and Dynamic Mechanical Analysis (DMA) tests performed on an epoxy-based single-component adhesive. The calibrated material model parameters were fed into a finite element simulation and the prediction results were compared to a unique set of experiments utilizing two substrate combinations of adhesive-bonded single lap shear joints. An excellent agreement between the simulated and experimental results (displacement across the bond, force applied by the adhesive) was achieved. The modeling results give a better understanding of the residual stresses and agree with the experimental trend on the effect of bondline thickness on the joint.

In the last two decades, the advances of using computers in sheet metal forming processes have introduced a novel adjustable process known as incremental sheet forming (ISF) as an optimal method for fast prototyping and low numbers of production. Formability and deformation behavior of ISF process are highly affected by the selected process parameters, such as the toolpath, step size, tool diameter, feed rate, and lubrication. The purpose of this work was to study the effect of these process parameters as well as hardening law on single point incremental forming (SPIF) process. For this work, a truncated-cone geometry was considered as a target shape with 7075-O aluminum alloy sheets. The simulations were conducted with different process parameters, i.e., toolpath type, step size, tool size, feed rate, friction coefficient, and wall angle with respect to the tool force and moment, effective plastic strain distribution and thickness of the part. In addition, three types of hardening laws i.e., isotropic extended Voce type hardening law, combined isotropic-kinematic Chaboche type hardening laws with single and double back-stress terms were applied in the finite element simulation of SPIF process. A detailed comparison of these hardening laws' predictions was made with respect to the tool force and moment, effective plastic strain distribution and thickness of the part.

A constitutive law was developed based on the evolutionary yield function to account for the evolution of anisotropy induced by the plastic deformation. For the effective description of anisotropy, the yield stress function and plastic potential were separately defined based on the non-associated flow rule. In particular, for the description of the equivalent status, the accumulated plastic work was employed as an alternative to the accumulated plastic strain. Numerical formulations based on the plastic work were also derived in case the hardening rule, as well as the evolution of the plastic potential and yield stress function, were defined in terms of the plastic work. The developed constitutive law was characterized using the mechanical properties of the multi-phase BAO QP980 steel and niobium sheets at room temperature. From the uniaxial tension tests and the balanced biaxial tension test, separate sets of anisotropic coefficients for each of the plastic potential and yield stress functions were obtained as a function of the plastic work. By comparing with non-evolving yield functions, the importance of the developed constitutive law to properly describe the evolution of the plastic potential and yield function were validated.

A systematic constitutive modeling and calibration methodology were developed based on rate-independent crystal plasticity to predict the quasi static macroscopic behavior of 3rd generation multiphase advanced high strength steels (3GAHSS) prepared with a quenching and partitioning (Q&P) process. In the constitutive law, martensitic phase transformation induced by the elastic-plastic deformation of the retained austenite is represented by considering the Bain strain, the lattice invariant shear deformation, and the orientation relationship between parent austenite and transformed martensite. The amount that each martensite variant evolves is obtained through an optimization scheme that constrains the plastic deformation of the retained austenite to have minimum-energy during phase transformation. In-situ high energy X-ray diffraction (HEXRD) tensile test data was utilized for the characterization and calibration of the material model. Dislocation density based hardening parameters were separately obtained for each phase by iteratively performing crystal plasticity finite element (CPFE) simulations until the simulated stress-strain curves matched the experimentally measured curves from in-situ HEXRD. The 3D representative volume element (RVE) for the 3GAHSS was generated by utilizing Dream.3D and the MTEX Matlab toolbox software. The distributions of grain size and crystal orientation were analyzed based on the measured EBSD data and accounted for in the generation of the 3D RVE. For verification and validation of the constitutive model, crystal plasticity finite element simulations of a uniaxial tensile test were performed using the developed material model and the generated 3D RVE. Additional hypothetical RVEs were also generated by manipulating phase volume fractions, phase transformation speed, and phase properties to determine if these virtual 3GAHSS steels have improved mechanical properties. Also, forming limit curves (FLC) for the multiphase 3GAHSS were predicted from the CPFE simulation results.

Designing multiphase metals based on their constituent phase micromechanical properties and using these metals for manufacturing lightweight automotive parks are a challenging process. A multiphase arid multiscale model is strongly beneficial in achieving this goal, as such a model can play an important role in connecting the material response at the macroscopic scale with the microstructural properties. In the present study, a computationally efficient rate independent crystal plasticity finite element (CPFE) model was used to simulate the bulging test of a three-phase (ferrite, martensite, and retained austenite) quenched and partitioned Q&P980 advanced high strength steel (AHSS) sheet. The CPFE model was developed to capture the mechanical properties of the steel phases based on their individual plastic deformation and slip systems. The macroscopic behavior of the polycrystalline aggregate was then predicted based on the volume averaged response of the representative phases, and their volume fraction in the steel sheet. In addition to random texture distribution assumption for each grain, two methods were considered in this study for the initial volume fraction distribution of the phases in steel sheet to introduce the effect of inhomogeneity based on phase distributions. The objective of developing the proposed model is to investigate the material behavior of the AHSS from the uniaxial microscale tension tests to large deformation applications through validation with the macroscale deformation based on the bulge test. The comparison between the multiphase CPFE model, experiments, and two phenomenological models (isotropic von Mises and anisotropic Hill'48 yield criteria) was conducted for validation of the proposed model. Also, the numerical results were further evaluated by comparing the predicted against experimental forming limit curve (FLC). The results showed that the trend of the forming limit curve predicted by the multiphase CPFE model is in good agreement with experimental results. (C) 2017 Elsevier Ltd. All rights reserved.

Austenite mechanical stability, i.e ., retained austenite volume fraction (RAVF) variation with strain, and transformation behavior were investigated for two third-generation advanced high-strength steels (3GAHSS) under quasi-static uniaxial tension: a 1200 grade, two-phase medium Mn (10 wt pct) TRIP steel, and a 980 grade, three-phase TRIP steel produced with a quenching and partitioning heat treatment. The medium Mn (10 wt pct) TRIP steel deforms inhomogeneously via propagative instabilities (Lüders and Portevin Le Châtelier-like bands), while the 980 grade TRIP steel deforms homogenously up to necking. The dramatically different deformation behaviors of these steels required the development of a new in situ experimental technique that couples volumetric synchrotron X-ray diffraction measurement of RAVF with surface strain measurement using stereo digital image correlation over the beam impingement area. Measurement results with the new technique are compared to those from a more conventional approach wherein strains are measured over the entire gage region, while RAVF measurement is the same as that in the new technique. A determination is made as to the appropriateness of the different measurement techniques in measuring the transformation behaviors for steels with homogeneous and inhomogeneous deformation behaviors. Extension of the new in situ technique to the measurement of austenite transformation under different deformation modes and to higher strain rates is discussed.

The dependence of the plastic anisotropy on the nominal strain rate for a medium-manganese (10 wt.% Mn) transformation-induced plasticity (TRIP) steel with initial austenite volume fraction of 66% (balance ferrite) has been investigated. The material exhibited yield point elongation, propagative instabilities during hardening, and austenite transformation to α′-martensite either directly or through ε-martensite. Uniaxial strain rates within the range of 0.005–500 s−1 along the 0°, 45°, and 90° orientations were selected based upon their relevance to automotive applications. The plastic anisotropy (r) and normal anisotropy (rn) indices corresponding to each direction and strain rate were determined using strain fields obtained from stereo digital image correlation systems that enabled both quasistatic and dynamic measurements. The results provide evidence of significant, orientation-dependent strain rate effects on both the flow stress and the evolution of r and rn with strain. This has implications not only for material performance during forming but also for the development of future strain-rate-dependent anisotropic yield criteria. Since tensile data alone for the subject medium-manganese TRIP steel do not satisfactorily determine the microstructural mechanisms responsible for the macroscopic-scale behavior observed on tensile testing, additional tests that must supplement the mechanical test results presented herein are discussed.

In conventional sheet metal forming processes, such as stamping, application of a two-dimensional (2D) plane stress yield function is sufficient as the out-of-plane stresses (sigma(zz), sigma(xz), sigma(yz)) are negligible and the deformation occurs under plane stress condition. However, in incremental sheet forming (ISF) processes, significant through-the thickness shears necessitates the use of a three-dimensional (3D) yield function to account for out-of-plane stress components. However, to calibrate the parameters of the non-quadratic anisotropic 3D yield function Yld2004-18p, out-of-plane normal and shear stresses are needed which are very difficult to obtain experimentally. In this study, the out-of-plane stresses were found using a three-dimensional (3D) representative volume element (RVE) developed from Electron Backscattered Diffraction (EBSD) images. By applying the crystal plasticity (CP) material model to these 3D RVEs, it was possible to perform computational experiments to generate the out-of-plane stresses required for the calibration of the Yld2004-18p yield function. To simulate the single point incremental forming (SPIF) of 7075-O aluminum alloy sheet, two different yield functions namely; Hill's 1948 and Yld2004-18p were used. A detailed comparison of the two yield functions' predictions was made with respect to different parameters, such as the tool force and moment, part thickness, development of stress and strain tensor components, and effective plastic strain distribution.

Nanoscale solute partitioning across multiple constituent phases in a 980-grade quenched and partitioned (Q&P) steel was analyzed using atom probe tomography (APT). The Q&P process was used to increase the C content in the retained austenite phase thereby improving its stability under plastic straining. Significant carbon enrichment of austenite was measured with decreased levels of C in martensite and almost depleted C content in ferrite, supporting the C partitioning mechanism in the literature. The APT analysis of retained austenite surrounded by martensite demonstrated a higher amount of C content compared with retained austenite surrounded by the ferrite phase. Lath and discrete carbide particle precipitation was also observed inside martensite colonies, tying up C and reducing the total amount of C available for austenite stabilization. In addition, the partitioning of Mn and other minor elements was quantitatively investigated by correlating APT and SEM-EBSD. These techniques provide a robust methodology for analyzing nanoscale compositional partitioning in multiphase steels, TRIP steels in particular, which can be used to better explain their microstructure-mechanical property relationships.

The effects of Coefficient of Thermal Expansion (CTE) mismatch in multi-material adhesive joints, induced during the manufacturing process, are expected to hinder the peak performance of the adhesive in the service life of the vehicle. With a goal to estimate these effects, this paper attempts to model the curing phenomenon of an adhesive and predict its mechanical properties using MAT_277 material model available in LS-DYNA, which serves as a good starting point towards modeling the cure history dependent viscoelastic behavior of adhesives. The adhesive is used to join two substrates of dissimilar metals and tested to capture the relative displacement of substrates. The experiments are performed on a specialized setup, which is built to perform experiments on lap shear joints. The curing kinetics model is calibrated using the results obtained by advanced experimental techniques like Differential Scanning Calorimetry (DSC); the mechanical properties are modeled by Generalized Maxwell model using Dynamic Mechanical Analysis (DMA) results. The fitted parameters are fed into MAT_277 to perform simulations of the lap shear joints tests. Finally, the calibrated model is validated by comparing the relative displacement in the steel-aluminum lap shear joint on a full curing cycle, similar to automotive paint baking oven, to experimentally obtained measurements using digital image correlation (DIC). The results of this work provide insights that will help in predicting the adhesive behavior over varying temperature-time histories during the manufacturing and in the service life of the vehicle.

In this study, the effects of strain rate on the mechanical properties and the strain-induced austenite-to-martensite transformation in type 201 austenitic stainless steel (SS201) were investigated. This grade was selected as a low-cost stainless steel with good lightweighting potential for automotive applications. The material was tested in tension at a quasi-static rate (5x10-2 s-1), two low-intermediate rates (100 s-1 and 101 s-1), and a high rate (5x102 s-1). 3D digital image correlation was used to enable accurate strain measurements during mechanical testing. Magnetic induction and X-ray diffraction were used ex-situ of deformation to measure the volume fraction of martensite formed at each strain rate, for different plastic strain levels. The effects of strain rate on deformation-induced martensite formation and on the stress/strain behavior was determined in this study, and was compared to results reported in the literature for 300 series austenitic stainless steels. The results show a favourable response for the SS201, which exhibits a substantial increase in strength and energy absorption at high rates without compromising tensile ductility.

Dynamic tensile testing using Kolsky Bar methods are used to assess crashworthiness of new structural materials needed for lightweight automotive design. High speed Digital Image Correlation (DIC) measurements routinely show that the strain experienced by dynamic tensile specimens deviates markedly from what is expected from the original strain wave analysis techniques used in tensile Kolsky bar metrology. Deviations can be manifest either by different average strain values over the gage section, or by departures from strain uniformity, or both. The former can be attributed to plastic yielding in the specimen outside the gauge section, while the latter concerns specimen geometry and material hardening effects. These issues are sometimes difficult to eliminate through simple modifications of the sample or the test design. Finally, it is of interest to make use of the data beyond necking, where the strain state departs significantly from ideal conditions. These metrology issues lend themselves to solution by inverse methods, where full field strain measurements and global load measurement data are available. In this paper we describe typical measurement data and explore methods to identify the constitutive response from dynamic tensile tests.

The dependence of the strain rate sensitivity of advanced similar to 1 GPa tensile strength steels on the phases present in their microstructures was studied by testing different steels at 0.005 and 500 s(-1). The high strain rate tests were performed using a Kolsky bar setup, while the quasi-static tests were performed using a universal testing machine. The two main steels of interest were the Ferrite-Martensite DP980 and the Ferrite-Martensite-Austenite QP980; the latter being a transformation induced plasticity (TRIP) assisted steel. For comparison, ferritic CR5 mild steel and austenitic stainless steel 201 were also tested under the same conditions. Though the differences in the steel chemistries were not taken into account, the results obtained here suggest a strong relationship between the phase-content of the steel and its response to the changes in the loading rate. The relationships between the observed mechanical behavior and the phases present in the microstructure are discussed.