Differential Work Hardening Research Articles

Failure prediction of AZ31B Mg sheet at room temperature considering material anisotropy and differential work hardening

Failure predictions of AZ31B Mg sheet at room temperature were conducted considering material anisotropy as well as differential work hardening for the range from uniaxial to balanced biaxial loading paths. The maximum shear stress criterion was used as a failure criterion, and both the associated and non-associated flow rules were employed along with the quadratic anisotropic functions to derive the analytic expressions for failure. Different levels of material anisotropy were considered in formulation, and procedures of determining the material coefficients considering the differential work hardening behavior were provided. Failure predictions using the analytical expressions were compared with the experimental results obtained by hemispherical dome tests. The results show that in the failure prediction of AZ31B Mg sheet, both the material anisotropy and the differential work hardening need to be addressed properly to make an accurate failure prediction.

Effect of anisotropy and differential work hardening on the failure prediction of AZ31B magnesium sheet at room temperature

In order to predict the failure of AZ31B Mg sheet at room temperature under uniaxial and biaxial loading paths, analytical expressions based on the maximum shear stress criterion in conjunction with the quadratic anisotropic yield function and plastic potential were developed. By utilizing the formulations based on the associated flow rule (AFR) and the non-associated flow rule (NAFR), different levels of material anisotropy were considered with the developed equations. Material coefficients of anisotropy were obtained from tensile and bulge tests taking into account the differential work hardening of AZ31B Mg sheet. Failure predictions were performed and compared with the experimental failure strains measured by the hemispherical dome tests at room temperature. In the failure prediction of AZ31B Mg sheet, it was found that the material anisotropy and the differential work hardening exhibited by the AZ31B Mg sheet were primary factors which have a major influence on the results of failure prediction, and the formulations based on the NAFR with the material coefficients obtained by taking into account the differential work hardening showed good accuracy by yielding failure predictions close to the experimentally measured failure strains.

3次スプライン降伏関数およびその異方硬化モデルの提案

3次スプライン降伏関数およびその異方硬化モデルの提案

Forming Limit Analyses of 590 MPa High Strength Steel Sheet Using Differential Work Hardening Model

A servo-controlled tension-internal pressure testing machine with an optical 3D deformation analysis system (ARAMIS®, GOM) was used to measure the multiaxial plastic deformation behavior of a 590MPa high strength steel sheet for a range of strain from initial yield to fracture. Tubular specimens were fabricated from the sheet sample by roller bending and laser welding. Many linear stress paths in the first quadrant of stress space were applied to the tubular specimens to measure the forming limit curve (FLC) and forming limit stress curve (FLSC), in addition to the contours of plastic work and the directions of plastic strain rates. It was found that the shapes of the measured work contours changed with the increase of work hardening (plastic work). The observed differential work hardening (DWH) behavior was approximated by changing the material parameters and the exponent of the Yld2000-2d yield function (Barlat et al, 2003) as a function of the equivalent plastic strain. The FLC and FLSC calculated using the Marciniak-Kuczyński-type (M-K) approach with the DWH model were in good agreement with the measurement.

Material Modeling and Springback Analysis Considering Tension/Compression Asymmetry of Flow Stresses

In-plane tension/compression tests of a dual phase steel sheet with a tensile strength of 780 MPa were carried out using in-plane stress reversal testing machine. Remarkable tension/ compression asymmetry of flow stress (TCA) has been observed. Moreover, biaxial tensile tests using cruciform specimens were performed to measure contours of plastic work. The test material exhibited differential work hardening (DWH). In order to reproduce the TCA, an asymmetric quadratic yield function proposed by Verma et al. (2011) was used. The parameters of the yield function were changed as a function of reference plastic strain to reproduce the DWH. Furthermore, to assess the springback prediction accuracy of the developed model, a 3-point bending experiment and finite element analyses (FEA) were performed. It is concluded that the use of the material model that is capable of reproducing DWH and TCA is a must for a highly accurate FEA of springback.

6000系アルミニウム合金板の異方硬化の定式と有限要素解析への適用

The deformation behavior of 6000 series aluminum alloy sheets under biaxial tension was precisely measured for linear stress paths, using servo-controlled biaxial tensile tests with both cruciform and tubular specimens. The tubular specimens were fabricated by bending and laser-welding as-received flat sheet materials. Differential work hardening (DWH) behavior was observed; the shapes of the contours of the plastic work constructed in the principal stress space changed with an increase in plastic work. A new constitutive model that can reproduce the DWH behavior was proposed; the model is based on the Yld2000-2d yield function with the exponent and material parameters changing as functions of plastic work. Finite element analysis of hydraulic bulge forming was performed using both the proposed DWH model and the conventional isotropic hardening model based on selected yield functions. The calculated results based on the DWH model were in closest agreement with the experimental results. Thus, the new constitutive model has been verified to be effective for improving the accuracy of the FEA.

Measurement and analysis of differential work hardening behavior of pure titanium sheet using spline function

Biaxial stress tests and in-plane tension/compression tests of pure titanium sheet (JIS #1) have been carried out in order to elucidate its anisotropic plastic deformation behavior under linear stress paths. Contours of plastic work and the directions of plastic strain rates at different levels of plastic work have been precisely measured in the stress space. The measured work contours bulged significantly toward the equibiaxial direction and showed strong asymmetry, and moreover, changed its shapes significantly with increasing plastic work (differential work hardening). Using the data of the measured work contours, the applicability of selected anisotropic yield functions, i.e., Hill’s quadratic, the Yld2000-2d and Cazacu’s yield functions, to the accurate prediction of the plastic deformation behavior of the pure titanium has been discussed. It was found that these yield functions were not able to reproduce the measured data. A new method for analyzing the differential work hardening behavior of the pure titanium sheet has been developed. This method uses the spline function of Bezier curves which approximates a work contour, inspired by the methodology proposed by Vegter and Boogaard (Int. J. Plasticity 22 (2006) 557-580). The procedure for determining the spline function is described in detail. The calculated results have been in good agreement with the differential work hardening behavior of the pure titanium sheet.

Measurement and Analysis of Ultra-Thin Austenitic Stainless Steel Sheet under Biaxial Tensile Loading and In-Plane Reverse Loading

Biaxial tensile tests of austenitic stainless steel sheet (SUS304) 0.2mm thick have been carried out using cruciform specimens. The specimens are loaded under linear stress paths in a servo-controlled biaxial tensile testing machine. Plastic orthotropy remained coaxial with the principal stresses throughout every experiment. The successive contours of plastic work in biaxial stress space changed their shapes progressively, exemplifying differential work hardening. The geometry of the entire family of the work contours and the directions of plastic strain rates have been precisely measured and compared with those calculated using conventional yield functions. Yld2000-2d [Barlat, F., Brem, J.C., Yoon, J.W., Chung, K., Dick, R.E., Lege, D.J., Pourboghrat, F., Choi, S.H. and Chu, E., International Journal of Plasticity, Vol. 19, (2003), pp. 1297-1319.] with an exponent of 6 was capable of reproducing the general trends of the work contours and the directions of plastic strain rates with good accuracy. Furthermore, in order to quantitatively evaluate the Bauschinger effect of the test material, in-plane tension/compression tests are conducted. It was found that the non-dimensional (σ /σu) - Δe /(σu/ E) curves measured during unloading almost fall on a single curve and are not affected by the amount of pre-strain, where σ is the current stress during unloading, σu is the stress immediately before unloading, Δe (< 0) is the total strain increment during unloading.

Influential microstructural changes on rolling contact fatigue crack initiation in pearlitic rail steels

Rail life is controlled by the balance between wear and fatigue damage due to in service loading. To model and optimise rail life, knowledge of the fatigue crack initiation mechanism is required. This paper reports the effect of in service loading on microstructural changes in the subsurface layer of pearlitic rail steels and observations of early stage (10–50 μm length) fatigue crack formation. Micro and nanohardness measurements are reported, along with microstructural observations, showing differential work hardening in the proeutectoid ferrite and pearlite phases. It is proposed that the differential straining results in ductility exhaustion in the proeutectoid ferrite and therefore fatigue crack initiation and initial growth in the proeutectoid ferrite phase. Observations of short (<50 μm) cracks in rails taken out of service containing significant amounts of proeutectoid ferrite (≈20%) confirm the proposed mechanism.

６０００系アルミニウム合金板の２軸引張塑性変形特性の測定と降伏条件式の検証

Biaxial tensile tests of 6000–type sheet aluminum alloy were carried out using newly designed cruciform specimens. The specimens were deformed under linear loading paths in a servo-controlled biaxial tensile testing machine. Plastic orthotropy remained coaxial with the principal stresses throughout every experiment. On the other hand, the successive contours of equal plastic work in biaxial stress space changed their shapes progressively, exemplifying differential work hardening. The geometry of the entire family of the work contours was compared with the yield loci calculated from existing yield criteria. The work contour at 0.0005 equivalent plastic strain almost coincided with the von Mises ellipse, while its curvature decreased as work-hardening progressed and became close to the Tresca-type yield locus. Moreover, it was observed that the directions of the measured plastic strain vectors were almost coincided with the associated normals to the current work contour in stress space; accordingly it appears that the work contours act as instantaneous plastic potentials at least under linear loading paths. The effect of age-hardening on the geometry of work contours was small.

Measurement and analysis of differential work hardening in cold-rolled steel sheet under biaxial tension

Abstract Biaxial tensile tests of cold-rolled steel sheet were carried out using newly designed cruciform specimens. The specimens were deformed under linear loading paths in a servo-controlled biaxial tensile testing machine. The maximum equivalent strain attained was 0.04. Plastic orthotropy remained coaxial with the principal stresses throughout every experiment. However, the successive contours of plastic work in biaxial stress space changed their shapes progressively, exemplifying a phenomenon which has been termed differential work hardening by Hill and Hutchinson (Trans. ASME J. Appl. Mech. 59 (1992) 1) and by Hill et al. (Int. J. Solids Struct. 31 (1994) 2999). The geometry of the entire family of the work contours was compared with the yield loci calculated from several existing yield criteria. Hill’s quadratic yield criterion overestimated the measured work contours; in particular, in the neighborhood of balanced biaxial tension, the discrepancy was large, while the other yield criteria described the behavior of the work contours well. The only yield criterion that could describe the general trends of the work contours as well as the in-plane r-value distribution with good accuracy was Gotoh’s biquadratic yield criterion. Moreover, it was observed that the components of an increment of logarithmic plastic strain are proportional to the components of the associated normal to the current work contour in stress space. Accordingly, it appears that the work contours act instantaneously as plastic potentials, at least under linear loading paths.

An investigation of plastic flow and differential work hardening in orthotropic brass tubes under fluid pressure and axial load

Thin-walled closed tubes of 70-30 brass were homogeneously deformed to finite levels of strain by internal fluid pressure combined with external longitudinal load in arbitrary fixed ratios. Plastic orthotropy was present initially and remained coaxial with the principal stresses throughout every experiment. On the other hand, the successive contours of equal work in biaxial stress space changed their shapes progressively. The geometry of the entire family is represented here by a simple formula involving only work-dependent parameters. The modelling is complemented by an empirical stress-strain relation for each experiment; the parameters in this case are dependent only on the imposed load ratio.In the present constitutive analysis a primary role is assigned to the contours of equal work (and not to yield loci). That role is further enhanced by our observation that (with certain exceptions) the successive contours act instantaneously as plastic potentials. This means that the components of an infinitesimal increment of logarithmic strain are proportional to the components of the associated normal to the current contour in stress space. In coming to this conclusion we found it advantageous to call in aid the geometric principle of polar reciprocity; as this rarely features in the mechanics literature an exposition ab initio is included in the paper.