Strength Differential Effect Research Articles

Strengthening behaviors and strength differential effect of nano-ZrB2-particle/AA6xxx alloy composites

This paper reports the correlation between strengthening behaviors and strength differential effect of nano-ZrB2-particle/AA6xxx alloy composites. The microstructures were characterized and mechanical properties of composites were investigated. This study examines the different strengthening behaviors under tension and compression. The changes of strain direction surrounding the nano-ZrB2 particles during the plastic deformation were analyzed with the aid of finite element analysis. The distribution of rotation angles of the strain directions indicates a different symmetric characteristic in compression and tension. The established relationship between strength differential effect and strengthening behaviors suggests that the asymmetry of strain surrounding the nano-ZrB2 particles during the deformation is responsible for the strength differential effect.

A Concept of Thermal Effort for Heat-Induced Metal Plasticity

This paper proposes a new concept of material effort that considers heat-induced plasticity for heat-resistant steels. These steels indicate a strength differential effect, a stress shearness effect, pressure sensitivity, and other features. Therefore, a three-parameter, temperature-dependent yield function was presented and, next, analytically and geometrically researched. To validate the accuracy of the formulated yield function, experiments were conducted with the designed specimens to characterize the heat-resistant steels St12T and 26H2MF, which underwent simple shear, uniaxial strain tension, and compression tests. The yield function was calibrated by using a simple analysis. Next, the calibrated constitutive equations were used to numerically determine the load–stroke responses of different tests. The numerical analysis showed that the proposed yield function based on three parameters could accurately describe the thermal effort in various loading conditions from the onset of yielding to the ultimate rupture. Accordingly, the proposed yield function is recommended to model material strength under various thermal loading conditions.

Modeling Strain Hardening of Metallic Materials with Sigmoidal Function Considering Temperature and Strain Rate Effects.

This study uses a sigmoidal function to describe the plastic strain hardening of metallic materials, considering temperature and strain rate effects. The effectiveness of this approach is evaluated and systematically compared with other hardening laws. Incorporating temperature and strain rate effects into the parameters of this sigmoidal-type hardening law enables a more precise description and prediction of the plastic deformation of materials under different combinations of temperature and strain rate. The temperature effect is coupled using a simplified Arrhenius model, and the strain rate effect is coupled with a modified Johnson-Cook model. The sigmoidal-type hardening law is integrated with an asymmetric yield criterion to address complex behavior, such as anisotropy and strength differential effects. The calibration and validation of the constitutive model involve examining uniaxial tensile/compressive flow curves in various directions and biaxial tensile/compressive flow curves for diverse metallic alloys, proving the proposed model's broad applicability.

Crystal plasticity finite element simulations on extruded Mg-10Gd rod with texture gradient

The mechanical properties of an extruded Mg-10Gd sample, specifically designed for vascular stents, are crucial for predicting its behavior under service conditions. Achieving homogeneous stresses in the hoop direction, essential for characterizing vascular stents, poses challenges in experimental testing based on standard specimens featuring a reduced cross section. This study utilizes an elasto-visco-plastic self-consistent polycrystal model (ΔEVPSC) with the predominant twinning reorientation (PTR) scheme as a numerical tool, offering an alternative to mechanical testing. For verification, various mechanical experiments, such as uniaxial tension, compression, notched-bar tension, three-point bending, and C-ring compression tests, were conducted. The resulting force vs. displacement curves and textures were then compared with those based on the ΔEVPSC model. The computational model's significance is highlighted by simulation results demonstrating that the differential hardening along with a weak strength differential effect observed in the Mg-10Gd sample is a result of the interplay between micromechanical deformation mechanisms and deformation-induced texture evolution. Furthermore, the study highlights that incorporating the axisymmetric texture from the as-received material incorporating the measured texture gradient significantly improves predictive accuracy on the strength in the hoop direction. Ultimately, the findings suggest that the ΔEVPSC model can effectively predict the mechanical behavior resulting from loading scenarios that are impossible to realize experimentally, emphasizing its valuable contribution as a digital twin.

Dynamic strength differential and Bauschinger effects in an extruded AZ80 magnesium alloy

Quasi-static and high-rate tension and compression properties of an extruded AZ80 Mg alloy rod were investigated at loading rates of 0.001 and 500 s−1. Acquired stress – strain results show that tension and compression plastic deformations of AZ80 rod are asymmetric, and such strength differential effect is dependent of strain rate and loading orientation. Strength differential effect is weakened at 500 s−1 when the sample was loaded along the extrusion direction. Crystal plasticity simulations on the basis of the visco-plastic self-consistent method were performed. Numerical results indicate that the rate and orientation dependency of strength differential effect in AZ80 alloy is related to {101‾2} extension twinning. High-rate tests for pretension, unloading and reverse compression were realized to investigate the dynamic Bauschinger effect. Experimental results show that Bauschinger effect of AZ80 alloy is anisotropic and sensitive to the strain rate. A Bauschinger effect parameter considering strength differential effect was proposed, and it was found that the Bauchinger effect in the extrusion direction is reduced significantly at 500 s−1.

Damage and fracture behavior under non-proportional biaxial reverse loading in ductile metals: Experiments and material modeling

This paper deals with a modified anisotropic stress-state-dependent plastic-damage continuum model incorporating combined hardening and softening rules to predict the plastic, damage, and fracture behavior of ductile metals under monotonic and reverse loading conditions. In the experimental part, a newly designed biaxially loaded cruciform flat HC-specimen of aluminum alloy EN AW 6082-T6 was subjected to biaxial non-proportional loading to generate a wide range of stress triaxialities during experiments. Thus, it is enabled to perform shear monotonic and reverse loading superimposed by various preloads without unloading processes. The experimental data reveal the Bauschinger effect, the strength-differential (SD) effect, and the change in the hardening ratio after shear reverse loading. This is captured by a Drucker–Prager-type yield criterion with an extended Voce isotropic hardening and modified Chaboche’s kinematic hardening rule. In addition, the damage surface is assumed to be translated in the direction of the rate of the damage strain. The numerically predicted global force–displacement curves and local strain fields are verified in terms of the digital image correlation (DIC) technique. Moreover, the scanning electron microscopy (SEM) is used to examine the fracture surfaces and to validate the proposed damage constitutive model.

Modeling of Eyld2000-2d Anisotropic Yield Criterion Considering Strength Differential Effect and Analysis of Optimal Calibration Strategy.

Sheet metals usually experience various loading paths such as uniaxial tension, uniaxial compression, biaxial tension, and simple shear during the forming process. However, the existing constitutive models cannot always accurately describe blanks' anisotropic yield and plastic flow behavior of blanks under all typical stress states. Given this, this paper improves the Eyld2000-2d yield criterion by introducing hydrostatic pressure to the A-Eyld2000-2d yield criterion that can describe the strength differential effect of materials. Meanwhile, to control the curvature of the yield surface more effectively, the near-plane strain yield stresses were added in the parameter identification process to calibrate the exponent m, so that the exponent is no longer considered as a constant value. Taking the widely used AA6016-T4, AA5754-O, DP980, and QP980 blanks in the automotive stamping industry as an example, the effectiveness of the new model and different parameter identification methods was verified by predicting experimental data under various simple and complex loading paths. Subsequently, the new model employing the optimal parameter identification strategy was compared with four widely used asymmetric yield criteria under associated and non-associated flow rules, including CPB06, LHY2013, S-Y2004, and Hu & Yoon2021, to further verify the accuracy of the proposed constitutive model. The results indicate that parameter identification strategy with variable exponent can significantly improve the flexibility of the yield criterion in describing the plastic anisotropy of blanks. Compared to the other yield criteria examined in this work, the new model provides the best prediction accuracy for the yield stresses and plastic flows of all blanks, especially in the near-plane strain and simple shear stress states. Modeling under the concept of anisotropic hardening can more accurately capture the evolving plastic behavior of blanks than isotropic hardening.

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.

Particle-matrix debonding with Strength-Differential effects

In this work the onset of failure caused by particle-matrix debonding in aluminum alloy 2090-T3 and magnesium alloy AZ31 under either overall uniaxial plane strain tension or compression load is studied numerically using a unit cell model. Especially for magnesium AZ31, experiments show a significant difference in the tensile-compressive yield stresses, the so-called Strength-Differential-effect (SD-effect). This SD-effect cannot be captured by any isotropic yield function and only by recent anisotropic yield functions. To accurately model AA 2090-T3 and magnesium AZ31 the general yield function by Yoon et al. (2014) is adopted in addition to the isotropic von Mises plasticity yield function and the anisotropic yield function of Hill (1948). The numerically predicted strain at which void nucleation initiates is generally found to be larger for magnesium AZ31 than for AA 2090-T3. However, depending on the orientation of the principal axes of plastic anisotropy this void nucleation strain varies significantly. This holds true for both materials, but the void nucleation strain of AA 2090-T3 in compression is numerically predicted to be practically identical whether or not isotropic or anisotropic plasticity is considered. In tension the void nucleation strain of AA 2090-T3 based on anisotropic plasticity is found to be more than double the strain obtained by von Mises plasticity. The numerically predicted void nucleation strain of magnesium AZ31 is significantly affected by the yield function adopted. For the von Mises yield function the value of the void nucleation strain is in between the predictions based on the anisotropic yield functions. For both tension and compression, the yield function of Yoon et al. (2014) results in the largest void nucleation strain, whereas the yield function of Hill results in the smallest strain value. This holds true for all five orientations of the principal axes of plastic anisotropy investigated.

Constitutive modeling of temperature and strain rate effects on anisotropy and strength differential properties of metallic materials

The thermal effects on tension compression asymmetry and anisotropy of several metallic materials with a hexagonal close-packed (HCP) crystal structure have been discussed in this study. The Yoon2014 asymmetric yield criterion is combined with a simple Arrhenius type temperature function and a modified Johnson-Cook strain rate model to formulate a thermal dependent plasticity model with analytical solutions for parameter calibration. The temperature and strain rate effects on the strength differential (SD) effects of both isotropic and anisotropic materials have been discussed. Both anisotropy and SD affect the shape of yield locus. In order to quantitatively distinguish the thermal effects on the strength differential and anisotropic effects of metallic materials, the evolution of yield locus and distribution of yield stress under two extreme scenarios has been discussed based on virtual experimental results. For the general application of the thermal dependent asymmetric plasticity model at different temperatures and strain rates, the calibration and validation of the model using uniaxial tensile/compressive results along different directions and biaxial tensile/compressive results have been elaborated for various metallic alloys.

Lode-dependent anisotropic-asymmetric yield function for isotropic and anisotropic hardening of pressure-insensitive materials. Part I: Quadratic function under non-associated flow rule

It is challenging to precisely model the complicated plastic deformation of metals, including anisotropy in strength and plastic deformation, strength differential effect, anisotropic hardening, etc. A new approach is proposed to extend anisotropic yield functions into asymmetric ones by introducing a Lode dependent function. The approach is applied to the Hill48 function with a Lode-dependent function in a form of the normalized third stress invariant. The proposed Lode-dependent anisotropic-asymmetric (LAA) is applied to characterize the anisotropic hardening behaviors under both tension and compression of QP1180, DP980, AA2008 T4 and α-Ti to verify its performance. The convexity of yield surface evolution with plastic deformation is investigated by a geometry-inspired numerical convex analysis method. The application shows that the proposed LAA function precisely characterizes the anisotropy in tension and compression and its evolution with plastic deformation. It is therefore suggested to model the anisotropic-asymmetric plastic behavior with its applications to metal forming.

Application of the upper bound theorem for metal forming processes considering an arbitrary isotropic pressure-independent yield criterion with no strength differential effect

Application of the upper bound theorem for metal forming processes considering an arbitrary isotropic pressure-independent yield criterion with no strength differential effect

Phase-field viscoelastic fracture modeling of polymer composites using strain tensor spectral decomposition

The mechanical behaviors of polymer composites exhibit strong time-dependent nonlinearities, and the tensile and compressive strengths can be vastly different. Such a strength differential effect poses a great challenge in fracture modeling using existing phase-field models. To address this problem, this study develops a new viscoelastic fracture phase-field model, in which the strain tensor spectral decomposition is proposed to decompose the elastic energy of the equilibrium and non-equilibrium branches into tensile and compressive components. The non-negativity of elastic energy and the thermodynamic consistency are theoretically verified. Various case studies, spanning from material uniaxial tension–compression and compression under isostatic pressure to fracture processes of realistic structural components, are used to validate the proposed method. Results of the proposed method are compared with those of existing methods and the actual testing data of polymer composites to demonstrate the effectiveness of the method. It is shown that the proposed method can accurately model not only the strong strength differential effect but also the isostatic pressure dependence of viscoelastic materials. Furthermore, the proposed method offers a more precise prediction of the fracture path and can deal with the loading rate effect.

Evaluation of loading-path-dependent constitutive models for springback prediction in martensitic steel forming

In this study, the performance of conventional and advanced constitutive models to the prediction of springback for ultra-high strength steel was assessed. The elasto-plastic behavior of a martensitic steel sheet sample was characterized to assess the conventional stress-strain behavior in uniaxial tension. More advanced tests such as uniaxial compression and tension-compression experiments were conducted to assess the strength-differential (SD) effect and hardening fluctuations during non-linear loading paths (NLLP effect). Three constitutive plasticity models, namely, the conventional isotropic hardening, Yoshida-Uemori (YU) two surface kinematic hardening and pure distortional hardening (HAH20) models were calibrated using an optimization procedure. Then, these models were employed for finite element predictions of springback after forming. The isotropic hardening model does not consider both SD and NLLP effects and the YU model captures only the influence of the NLLP effect. On the other hand, the HAH20 model describes both effects simultaneously. The performance of these models with respect to springback prediction was evaluated using three forming applications: wiper bending, C-rail drawing and Roof-Side-Rail crush forming. This work indicates that the HAH20 model is the best candidate for the prediction of forming and springback for such martensitic steel because of its ability to consider both SD and NLLP effects. However, the conventional isotropic hardening model led to results in good agreement with those obtained using the HAH20 model in specific cases. The reason, discussed in detail in this article, is likely due to the compensation of the permanent softening due to load reversal by the higher flow stress due to the SD effect.

A stress-state-dependent damage criterion for metals with plastic anisotropy

The paper discusses the effect of stress state and of loading direction on the onset and evolution of damage in anisotropic ductile metals. A series of experiments with uniaxially and biaxially loaded specimens covering a wide range of stress states and different loading directions is used in combination with corresponding numerical simulations to develop damage criteria. The underlying continuum damage model is based on kinematic definition of damage tensors. The strain rate tensor is additively decomposed into elastic, plastic and damage parts. The anisotropic plastic behavior of the investigated aluminum alloy sheets is governed by the Hoffman yield condition taking into account the strength-differential effect revealed by uniaxial tension and compression tests. Based on this yield criterion generalized anisotropic stress invariants as well as the generalized stress triaxiality and the generalized Lode parameter are defined characterizing the stress state in the anisotropic ductile metal. A damage criterion formulated in terms of these anisotropic stress invariants is proposed and damage mode parameters allow adequate consideration and combination of different damage processes on the micro-level. At the onset of damage the anisotropic stress parameters are determined. With these experimental-numerical data the damage mode parameters are identified depending on stress state and loading direction.

Modelling in materials behavior of strength differential effect and yield locus evolution with non-associated flow rule

During numerical simulation of sheet metal forming, the accurate models to describe material yielding and hardening behavior by considering the anisotropy, non-uniform evolution of the yield surface and strength differential effect are vital to predict complicated deformation and forming defects such as fracture and springback. In the present work, a novel yield model with non-associated flow rule is proposed based on the frame of S-Y2009 criterion and coupled with normal stress components and the second deviatoric stress invariants, where the former is used to describe the anisotropy and non-uniform evolution of yield loci, and the later enables the description of SD effect. Different from some other models which identify the parameters via optimization algorithms, the proposed model adopts an analytical identification method from the stress-strain curve in various loading conditions, including uniaxial tension and compression along 0°, 45°, 90° to the rolling direction, and equi-biaxial tension and compression. The flexibility of the proposed model is validated for high strength steels, aluminum alloys and titanium alloys.

Modeling stress anisotropy, strength differential, and anisotropic hardening by coupling quadratic and stress-invariant-based yield functions under non-associated flow rule

An accurate description of yield surface is essential for the high-fidelity numerical analyses of sheet metal forming processes. In this work, a simple coupling of anisotropic quadratic and isotropic stress-invariant-based yield functions is proposed under the non-associated flow rule. The quadratic part is the asymmetric Hill48 function, which describes the anisotropic hardening with explicitly calibrated parameters from stress-strain curves. A new stress-invariant-based yield function, as a second component, is developed to capture the shapes of yield surface for diverse metallic materials with enhanced flexibility. Finally, a yield function is established by multiplying the anisotropic quadratic and the isotropic stress-invariant-based parts, which satisfies the convexity requirement in terms of stress state. The proposed asymmetric anisotropic yield function is validated with automotive sheet metals including dual-phase steels, aluminum alloys and magnesium alloys. Results show that the new yield criterion can accurately predict the anisotropy in stress, strength differential effect and yield surface evolution (or anisotropic hardening) of the investigated sheet metals.

A general yield function with differential and anisotropic hardening for strength modelling under various stress states with non-associated flow rule

Sheet metal experiences various stress states during plastic deformation, including uniaxial compression, shear, uniaxial, plane strain and equibiaxial tension, but the existing yield functions cannot precisely model the differential strain hardening behaviour under different stress states. In this research, a stress invariant-based yield function is proposed to illustrate differential hardening by an analytical appraoch under distinct stress states (eg. from uniaxial compression to equibiaxial tension). The convex domain of the proposed function is computed by a simple geometry-inspired numerical convex analysis method. The parameters of the function are analytically computed by hardening behaviours under four different stress states from uniaxial compression to equibiaxial tension, such as uniaxial tension, equibiaxial tension, shear and plane strain tension. The proposed function is utilized to describe the plastic behaviour of AA7075 T6, a high strength steel QP1180, and a magnesium alloy AZ31 under the four different stress states from the onset of plastic deformation to fracture. Simulations with the proposed function are conducted to predict the load response of experiments in shear and notched tensile tests. The function is further extended into anisotropic hardening by interpolation method with the Barlat’91 linear transformation tensor. The result shows that the experimental responses are precisely predicted from the proposed yield function under various stress states in the entire range of plastic deformation. The application to BCC, FCC and HCP metals suggests that the proposed function is capable of precise modelling of differential hardening behaviours under four different stress states and strength differential effect and its evolution.

On the Effect of the Tension-Compression Ratio on Forming of Isotropic Materials

It is generally believed that the choice of the yield criterion used to describe the plastic behaviour of isotropic metallic materials does not affect much the accuracy of the predictions of forming operations. For this reason, the von Mises yield criterion is widely used for modelling their plastic behaviour. However, according to the von Mises yield criterion, the ratio between the yield stresses in tension and compression is always 1.0. Nevertheless, materials can present same asymmetry, i.e. a strength differential (SD) effect. In this work, the yield criterion proposed by Cazacu et al. [1], is adopted to describe the mechanical behaviour of isotropic materials, with different levels of tension-compression asymmetry. Numerical simulations of the deep drawing of a cylindrical cup were performed considering these different virtual isotropic materials, in order to evaluate its impact on the thickness distribution and cup height. The analysis of the stress and strain paths, for material points initially located in the flange is performed, enabling the correlation between the thickness distributions predicted and the plastic strain ratios obtained analytically, using the yield function and the normality rule. The results show that even small changes in the tension-compression stress ratio can influence the strains distribution, in isotropic materials.

Analysis of ductile damage and fracture under reverse loading

This paper investigates the influence of reverse and cyclic loading on the damage and fracture behavior of the aluminum alloy EN-AW 6082-T6. A series of uniaxial tension–compression and shear tests with newly designed shear specimen has been performed to analyze the development of plastic deformations and damage under different stress conditions. In addition, several monotonic uniaxial tension and compression tests are conducted to detect the strength-differential (SD) effect. Hence, combined hardening law is incorporated into the hydrostatic-stress-sensitive yield function to predict irreversible deformations under cyclic loading. A newly defined strain triaxiality is proposed to describe the strain state and to reveal the damage evolution processes. To accurately model cyclic plasticity, strain triaxiality is incorporated into the extended Voce strain hardening, and the angle parameter between effective back stress and reduced stress is added to Chaboche’s kinematic hardening. Furthermore, a modified anisotropic stress-state-dependent continuum damage model is considered to evaluate the damage and fracture evolution processes. Additionally, the digital image correlation (DIC) technique is applied to measure the strain fields during the experiment. Numerical simulations are used to predict the distribution of stresses and strains. Finally, the distribution and amount of damage are used to explain the fracture behavior detected by scanning electron microscopy (SEM) pictures taken in the critical parts of the specimens. SEM images and numerically predicted damage stains confirm that the different failure modes depend on the loading history.