Strength Differential Effect Research Articles

Experimental study on the fracture behavior of AZ91D magnesium alloy under complex loading

In this study, quasi-static compression, tensile, shear, and combined compression-shear tests are conducted on cast AZ91D magnesium (Mg) alloy to study its fracture behavior. Shear-compression specimens are applied instead of complex loading device to obtained the fracture response of Mg alloy under mixed compression/shear tests. Results show that the stress states of specimens can be controlled by changing the loading angle. The strength differential effect is observed, and the criterion with von Mises form cannot give an appropriate description of the fracture behavior of Mg alloy for its dependence on the direction of normal stress. The criterion with the form of odd function and that contains two deviatoric stress invariants is utilized to describe the fracture behavior of Mg alloy. In addition, the effect of pressure term and the direction of normal stress on the fracture strength of Mg alloy are commonly mistaken for the other, and the detailed method to distinguish these two effects has been conducted on the basis of the criteria of f =(J2,J3) and f =(I1,J2,J3).

Enhancement of Accuracy of Springback Simulation Using the Material Model Considering the Strength Differential Effect

Enhancement of Accuracy of Springback Simulation Using the Material Model Considering the Strength Differential Effect

Experimental and Numerical Bendability Analysis of a 3rd Generation Magnesium Alloy

Motivated by the demand for lightweight materials, magnesium alloys in use for structural components in the automotive and aircraft industry are getting attention. In the current contribution, the bendability of the innovative magnesium alloy “E-form” AZ31 at room temperature is investigated by means of 3-point bending tests and respective numerical simulations. The bending tests were conducted for different orientations of the sample with respect to the sheets axes of orthotropy. The force-displacement records confirmed the plastic anisotropy of the material evidenced in tensile testing. The limits of bendability were given by cracking of the samples, which was found to be strongly direction-dependent. A correlation between bendability and Lankford coefficient was explored. The elastic-plastic deformation was modelled using finite elements and a two-yield-surface model, which is able to describe the evolving strength differential effect and the anisotropy. Approaches based on 1D, 2D and 3D discretisations were compared. Zones with tensile and compressive stresses were identified by microstructural changes and mapped with its numerically obtained counterparts.

An Extended Drucker Yield Criterion to Consider Tension–Compression Asymmetry and Anisotropy on Metallic Materials: Modeling and Verification

Pressure sensitive asymmetric Drucker yield criterion is developed to deal with pressure dependent sheet metals for instance steels and aluminum alloys. The sensitivity to pressure is conserved by introducing three-dimensional anisotropic parameters in the first stress invariant; while the third deviatoric stress invariant is remained in odd function form to consider the strength differential effect (SDE). To describe the flow stress directionalities of metallic materials, the Drucker yield function is extended using two transformation matrix consisting of anisotropic parameters. The proposed Drucker yield criterion is utilized to predict the anisotropic yield and plastic deformation of aluminum alloys with weak SDE: AA 2090-T3 with face-centered cubic (FCC) crystal systems and AA 2008-T4 with body-centered cubic (BCC) crystal systems as well as metals with strong SDE: Zirconium clock-rolled plate with hexagonal close packing (HCP) crystal systems. The comparison between the predicted anisotropic behavior and experimental results reveals that the extended anisotropic Drucker yield criterion can precisely model the anisotropy for FCC, BCC and HCP metals. The proposed function is implemented into ABAQUS VUMAT subroutines to describe the four-point bending test which is used to consider the effect of various yield functions and material orientations on deformation behavior. The obtained contours of the cross-section, strain components distribution and also the shift of neutral layer indicate that the extended Drucker yield function can well predict the final geometric configuration of the deformed Zirconium beam.

An enhanced distortional-hardening-based constitutive model for hexagonal close-packed metals: Application to AZ31B magnesium alloy sheets at elevated temperatures

In this study, a new material model for hexagonal close-packed (HCP) metals for predicting their flow responses under monotonic/cyclic loadings at various temperatures is proposed. The temperature-dependent constitutive model is re-formulated using a continuum-based distortional hardening law, which affects the shape of the yield surface depending on the loading direction, and also uses the concept of the dominant deformation modes in magnesium alloys: twin, untwin, and slip-dominate modes, considering the role of the twins in plastic deformation. In terms of the material asymmetry in yield strength, the Cazacu–Barlat–Plunkett (CPB) ’06 yield criterion is extended to include thermal effects. A numerical formulation of the material model has also been developed to allow its implementation into finite element analysis software via a user-defined material subroutine (UMAT). The predicted results of stress–strain response for monotonic and cyclic loadings are excellent agreement with the experimental data. Moreover, the simulated results show the strength differential (SD) effect and unusual flow responses of AZ31B magnesium alloy sheets at room temperature, as well as the variation in the SD effect and anisotropic hardening behavior at elevated temperatures.

Ductile fracture prediction using enhanced CDM model with Lode angle-dependency for titanium alloy Ti-6Al-4V at room temperature

Abstract Fully coupled ductile damage model considering strength-differential (SD) effect is proposed for simulation of metal forming processes for Ti-6Al-4V. The developed constitutive equations are based on non-associative plasticity theory under thermodynamically-consistent framework. The third stress invariant is added to Hill48 criterion to capture the SD effect. Lode angle-dependent enhanced fully coupled damage model is proposed to account for the loading path sensitivity on ductile damage initiation and growth. A detailed material parameters identification procedure is presented. The proposed model is implemented into the FE code Abaqus/Explicit through user defined subroutine VUMAT. The numerically predicted results obtained with the proposed model are compared to experimental data of Ti-6Al-4V and good agreement is observed.

Impact of distortional hardening and the strength differential effect on the prediction of large deformation behavior of the Ti6Al4V alloy

The ability of three plasticity models to predict the mechanical behavior of Ti6Al4V until fracture is presented. The first model is the orthotropic yield criterion CPB06 developed by Cazacu et al. (Int J Plast 22:1171–1194, 2006) with a distortional hardening, allowing for the description of material anisotropy and the strength differential effect. The second model is the anisotropic Hill’48 yield criterion with distortional hardening, describing the material anisotropy with quadratic functions but is unable to model the strength differential effect. Finally, the third model is the classical Hill’48 yield locus with isotropic hardening. Distortional hardening is modeled through five yield surfaces associated with five levels of plastic work. Each model is validated by comparing the finite element predictions with experimental results, such as the load and displacement field histories of specimens subjected to different stress triaxiality values. Tensile tests are performed on round bars with a V-notch, a through-hole, and two different radial notches; compression tests are performed on elliptical cross-section samples. The numerical results show that none of the models can perfectly predict both the measured load and the sample shape used for validation. However, the CPB06 yield criterion with distortional hardening minimizes the global error of the model predictions. The results provide a quantification of the influence of mechanical features such as hardening phenomenon, plastic anisotropy, and tension–compression asymmetry. The impact of these features on the prediction of the post-necking deformation behavior of the Ti6Al4V alloy is explored.

On the use of heterogeneous thermomechanical and thermophysical material properties in finite element analyses of cast components

Cast components generally show a heterogeneous distribution of material properties, caused by variations in the microstructure that forms during solidification. Variations caused by the casting process are not commonly considered in structural analyses, which might result in manufacturing of sub-optimised components with unexpected in-use behaviour. In this paper, we present a methodology which can be used to consider both thermomechanical and thermophysical variations using finite element analyses in cast components. The methodology is based on process simulations including microstructure modelling and correlations between microstructural features and material properties. Local material data are generated from the process simulation results, which are integrated into subsequent structural analyses. In order to demonstrate the methodology, it is applied to a cast iron cylinder head. The heterogeneous distribution of material properties in this component is investigated using experimental methods, demonstrating local variations in both mechanical and physical behaviour. In addition, the strength-differential effect on tensile and compressive behaviour of cast iron is considered in the modelling. The integrated simulation methodology presented in this work is relevant to both design engineers, production engineers as well as material scientists, in order to study and better understand how local variations in microstructure might influence the performance and behaviour of cast components under in-use conditions.

The Effect of Strength Differential on Material Effort and Lifetime of Steam Turbine Rotors Under Thermo-Mechanical Load

The paper presents the results of experimental tests and numerical simulations related with the strength differential effect. Tensile and compression tests on 2CrMoV low-alloy steel are performed to evaluate the magnitude of the yield stress difference in tension and compression. The strength differential parameter is then used in the formula for equivalent stress proposed by Burzynski. The material effort calculated using Burzynski and Huber-Mises-Hencky hypotheses was compared for different start-stop cycles. Analytical notch stress-strain correction rules by Neuber and Glinka-Molski were applied to compute elastic-plastic strain amplitudes in rotor circumferential grooves. It was finally shown that the strength differential effect has significant influence on the predicted fatigue life under thermo-mechanical loading.

A criterion for general description of anisotropic hardening considering strength differential effect with non-associated flow rule

An accurate description of the material yielding behavior is of great importance for a trustworthy prediction of complicated forming processes via numerical analysis. For metal sheets, the work hardening rate, in general, varies according to the loading directions and conditions due to the texture developed during cold rolling processes, and accordingly, the yield surface evolves with a variation of its shape and size during plastic deformation. The non-uniform evolution of the yield surface becomes a non-negligible issue especially for the materials showing the severe tension/compression asymmetry on the yielding behavior with respect to the loading direction. A primary concern here is that the advanced yield criteria previously developed normally feature an isotropic expansion of the yield surface which is determined at an initial yielding stage and thereby neglect the evident changes in the shape of the yield surface as implied by experimental tests. In this paper, a solution to the challenge of modeling a general criterion, which accurately describes the evolution of the anisotropy/asymmetry-induced distortional yielding behavior, is proposed using neither any interpolation nor optimization techniques for the calibration of the yield surface. The new criterion is proposed based on the Stoughton and Yoon (2009) criterion, which features non-associated flow rule, with the multiplication of two additional terms referred to as scaling and asymmetry functions. The proposed criterion was successfully applied to various types of metallic materials to validate its noticeable flexibility and general applicability in describing the anisotropic/asymmetric yielding behavior. An extensive comparison of the experimental results with the predictions from the proposed criterion reveals that the proposed criterion provides sufficient predictability on the subsequent evolution of the anisotropy/asymmetry-induced distorted yield surface for various metallic materials over a broad range of plastic strain level, strain rate, and temperature.

Indentation Size Effect in Pressure-Sensitive Polymer Based on A Criterion for Description of Yield Differential Effects and Shear Transformation-Mediated Plasticity.

Indentation size effects in poly(methyl methacrylate) (PMMA) were studied through nanoindentation. Two factors of indentation size effects in PMMA, namely yield criterion and shear transformation-mediated plasticity, were analysed in detail. The yield criterion that considers strength differential (SD) effects and pressure sensitivity was constructed by performing the combined shear-compression experiments. The relationship between hardness and normal stress can then be obtained based on Tabot’s relation. Shear transformation-mediated plasticity was also applied to model the measured hardness as a function of the indentation depth at different strain rates. Results show that the yield criterion contains the terms of SD effects and pressure sensitivity gives the best description of the yielding of PMMA. Additionally, the volume of single shear transformation zone calculated through the presented criterion agrees well with simulation and exhibits increases with increasing strain rate. Indentation size effects in PMMA under different strain rates were discussed and an appropriate indentation depth range was suggested for calculating the hardness and modulus.

Modelling and simulation of ductile failure in textured aluminium alloys subjected to compression-tension loading

The effects of strain path change on the ductile failure process of textured aluminium alloys are investigated through reversed loading experiments and finite element-based unit cell simulations. Three extruded aluminium alloys (AA6060, AA6082.25 and AA6082.50) are solution heat-treated and artificially aged to three different conditions, namely temper O (annealed), temper T7 (overaged) and temper T6 (peak strength). Compression-tension experiments on diabolo-shaped specimens are conducted including five different pre-compression levels (0, 10, 20 30, 40%), i.e., the specimens are first compressed to a prescribed strain and then reloaded to fracture in tension. The materials are modelled with an advanced plasticity model accounting for plastic anisotropy, non-associated plastic flow, nonlinear isotropic and kinematic hardening, strength differential effect, and transient and permanent effects of strain path change. Crystal plasticity finite element analyses are performed to determine the plastic anisotropy of the materials and then used to calibrate the anisotropic yield surfaces, whereas the work-hardening response is calibrated from the experimental data. The effects of grain morphology and precipitate structure on the plastic anisotropy are neglected. Finite element simulations of all the reversed loading tests are performed and the non-proportional loading history from the centre of the specimen is extracted. These non-proportional loading histories are imposed to a unit cell model with a central spherical particle to study the effect of pre-compression on the ductile failure process, where the initial plastic anisotropy and the work-hardening behaviour after strain path change are accounted for. The strain to coalescence of the three-dimensional unit cell is mapped back to the reversed loading tests to determine the logarithmic strain to failure after the strain path change, and the numerical results are compared with the experimental data. The unit cell model predicts an approximately constant tensile ductility with pre-compression for the different materials. Variations are observed between the materials as the strength, work hardening and anisotropy are found to influence the response of the unit cell differently and affect the tensile ductility after the pre-deformation. In the experiments, the tensile ductility is largely constant or exhibits a small increase for the majority of the materials, but for some alloy-temper combinations a larger increase is observed, which is not captured in the unit cell computations.

Verification Simulation Considering Strain Rate Dependency and Strength-Differential Effect of PA66 Nylon

Verification Simulation Considering Strain Rate Dependency and Strength-Differential Effect of PA66 Nylon

Investigation of S-D effect on plastic flow behavior of Armox 500T steel

Quasi-static compression and tensile tests were conducted on Armox 500T steel in the range of strain rates from 10−4 to 10−1 s−1 to evaluate strength differential (S-D) effect. Dynamic flow behavior under compressive loading conditions at strain rates of 102–103 s−1 was measured by conducting a series of tests on split-Hopkinson pressure bar setup. Further, J–C material model parameters have been established considering static and dynamic compression test data at strain rates of 10−3–103 s−1. Subsequently, FE modeling was carried out to validate J–C material model parameters and compared with the set of previous studies. The comparative study revealed the presence of S-D effect on the plastic flow behavior of the test material. Strain–time pulse as well as stress–strain response of Armox 500T steel obtained from simulation had a good agreement with the experimental results. The data generated from the present work will be helpful in the design and development of armor vehicles and other military structures against different threat scenarios.

Validation of recent analytical dilatational models for porous polycrystals using crystal plasticity finite element models with Schmid and non-Schmid activation laws

Recent analytic criteria for isotropic porous materials developed by Cazacu et al. (2013) revealed the importance of considering specificities of plastic behavior in the matrix. On one hand it was shown that if the matrix material is governed by the von Mises criterion, the yield surface of the porous material should be centrosymmetric and, with the exception of hydrostatic and purely deviatoric loadings, there are combined effects of the mean stress and third-invariant of the stress deviator on void growth or collapse; but on the other hand if the matrix plastic deformation displays strength differential (SD) effects, the response is also sensitive to third-invariant and there is a lack of symmetry of the yield surface of the porous material. In this paper, we use a unit cell modeling approach in conjunction with a crystal plasticity finite element model to verify these theoretical predictions. It is assumed that each porous polycrystal contains a regular array of initially spherical voids and a random initial texture. At the grain-level, we consider that plastic deformation is governed by Schmid law and a recent non-Schmid formulation by Savage et al. (2017a) that intrinsically accounts for tension–compression asymmetry in a physical sense. Unit cell FE calculations are performed for axisymmetric tensile and compressive loadings corresponding to a fixed value of the stress triaxiality and the two possible values of the Lode parameter. The resulting numerical points representing the homogenized yield surfaces and void growth/collapse curves are found to be in agreement with the analytical model's predictions.

Inverse identification of constitutive parameters with instrumented indentation test considering the normalized loading and unloading P-h curves

The feature of instrumented indentation test (IIT) makes it suitable for the characterization of local constitutive behavior in a small volume of solids. In the present study, the relationship between the shape of the normalized loading P-h curve and the indenter tip rounding radius, and the influences of the constitutive parameters of a Ludwik-type isotropic hardening model on the shape and the initial slope of the normalized unloading P-h curve were investigated by theoretical analysis and sophisticated numerical sensitivity analysis. From the analytical results, a two-stage analytical approach that can inversely identify multiconstitutive parameters simultaneously was proposed. In the first stage, by considering the least-square distance between the experimental and the simulated normalized loading P-h curves (g(h/hmax)) as the objective and C1 in the tip area function as the input variable, the tip rounding was identified by a single-objective optimization procedure. With the optimal tip rounding, a multiobjective optimization procedure was then performed to identify the constitutive parameters of the target materials. The initial slope of the normalized unloading P-h curve (ΔS’(P/Pmax-h/hmax)), absolute value of the differences between the simulated and the experimental maximum load (ΔPmax), initial slope of the unloading P-h curve (ΔS), and contact hardness (ΔH) were set as objectives, while all the material parameters except the Poisson's ratio (v) were considered as input variables. Results of the numerical verification with a set of arbitrarily selected constitutive parameters and the experimental verification on Ti-18 (a near-β high-strength titanium alloy) fit fairly well with uniaxial tensile parameters. With regard to T40, the identified true stress-true plastic strain curve is about 20% higher than the uniaxial tensile curve. One possible explanation is the occurrence of the strength differential and anisotropy effects during the plastic deformation process of α-phase titanium. It is worthy to be noticed that the present study may propose a new way to calibrate the tip area function directly on the target material without any standard indentation sample and improve the quality of the identification of the material constitutive parameters by IIT.

Thermodynamically-consistent constitutive modeling of hardening asymmetry including isotropic ductile damage for Mg alloys

It is well known that the Mg alloys exhibit strong initial anisotropy and hardening asymmetry during plastic flow. These behaviors are mainly caused by their Hexagonal Close-Packed (HCP) lattice structure and the activation of deformation twinning. In this paper, a thermodynamically-consistent plasticity model is proposed to capture the strong anisotropic/asymmetric behavior of Mg alloys with considering the effect of isotropic ductile damage. A detailed calibration method of the proposed model is provided using shear, tension and compression tests along different orientations of the rolled sheets. The material parameters related to initial anisotropy and strength-differential (SD) effect is treated separately from the hardening and damage parameters. The identification procedure is based on minimizing the difference between experimental measurements and FE simulation results over the whole deformation process until final failure. The parametric study of the newly proposed model is conducted to demonstrate its capability in capturing the hardening asymmetry. The predictive capabilities of the proposed model are illustrated through application to two Mg alloys (AZ31B and ZEK100), both the initial tension-compression asymmetry and unusual stress-strain response under monotonic compression are accurately predicted.

Evaluation of tension-compression asymmetry of a low-carbon steel sheet using a modified classical compression test method

A modified classical compression test method was used to examine in-plane tension-compression asymmetry in a low carbon steel sheet. In this compression test method, interfacial friction between the compression platens and specimen surfaces was significantly reduced by use of polycrystalline diamond plates installed on the compression dies. Furthermore, crosshead displacement of the universal testing machine, which inherently includes deflection of the machine itself, was corrected to the net deformation of the specimen based on a series spring model. Consequently, precision of the compressive strains obtained with the present test method is equivalent to that attained in the standard tension tests using wire strain gauges. For tension and compression tests performed at in-plane directions of 0°, 45° and 90° relative to the rolling direction (RD), significant tension-compression asymmetry (i.e. strength differential effect (SDE)) was observed. In all the mechanical tests in the three testing directions, flow stresses in tension tests were smaller than those in compression tests.

High accuracy springback simulation by using material model considering the SD effect

In order to enhance the accuracy of springback simulation, the strength differential (SD) effect, i.e., the difference in flow stress between tension and compression, of a high strength cold-rolled steel sheet with a tensile strength of 980 MPa is measured by means of in-plane tension-compression test apparatus. Bi-axial stress tests are also performed to measure the contour of plastic work of the test material. From those experimental results, the material model which can consider the SD effect is determined. Furthermore, this material model is implemented into commercial FEM code by using user-subroutine function. To check the validity of this model and established FEM analysis system, curvature-hat crush forming experiment is performed. By comparing the experimental result and forming simulation result, the accuracy of the material model which can consider the SD effect is validated. Consequently it is concluded that the use of material model which is capable of reproducing the SD effect is a must to enhance the accuracy of springback simulation.

Study on the influence of orthotropy and tension–compression asymmetry of metal sheets in springback and formability predictions

Most yield criteria possess a point-symmetry with respect to its center, meaning that a stress state and its reverse state have the same absolute value. However, this can be an unrealistic approximation, even for cubic metals (both face-centered cubic and body center cubic)), which can present a small asymmetry between the yield stress in tension and compression, i.e. a strength differential (SD) effect. This work analyzes the influence of taking or not into account the SD effect in the modeling of the sheet orthotropic behavior in the numerical simulation of a cylindrical cup drawing process. The yield criterion adopted is the CPB06 [1], including its version with two linear transformations [2], allowing a better fitting of the experimental data available. The material analyzed presents a quite small tension-compression ratio of 0.963. However, this small SD effect leads to a slightly higher punch force during the bending dominated stage, resulting in a very small influence on the springback prediction. The influence on the thickness evolution during the process is negligible.