Analysis of the formability magnesium alloys using a new ductile fracture criterion

An innovative methodology for the determination of forming limits is proposed, based on the strain energy density criterion. In the first section of this paper a modification of the strain energy density criterion, that has mainly been applied for crack propagation in fracture mechanics, is performed, in order to become applicable in metal forming processes. In the second section, experimental methods and Finite Element (FE) analysis for the case of deep drawing forming process are used for the verification of the methodology. Based on the simulation methodology, the forming limits and some process parameters namely, forming temperature, punch radius, punch profile radius and strain rate sensitivity of magnesium alloys AZ31 and WE43 are determined. The optimization results for the studied case show that magnesium alloys have limited formability especially at room temperature; however the formability can be improved by forming at higher temperatures. Finally, formability is improved as the punch and punch profile radii increase up to an optimum value.     

Analysis of ductile tearing using a local approach to fracture

In this paper, the Rice and Tracey (RT) model based on growth of cavities is verified in order to describe the ductile tearing in stainless steel 12Ni6Cr and aluminium alloy. Experimentally, central crack panel and compact tension specimens were tested. The comparison of the experimental results with the classical RT model shows that this model cannot make a good prediction using J −Δ a curve. On the basis of fitting procedure and numerical simulations, we have proposed a modification of this model by introducing corrective coefficients to improve the classical RT model. The proposed model, although very simple, is able to approximate with good accuracy the experimental results and that the approximation is, as expected, better than using the RT approach directly.     

A micromechanical analysis of a local failure criterion for particle-reinforced composites

The present paper aims at predicting the ultimate mechanical properties of a particle-reinforced polymer using a micromechanical approach of a local failure criterion. The considered criterion includes both normal and shear stresses at the interface between the polymer matrix and the reinforcing material. In the case of rigid particles, a new closed-form expression of the interfacial stress concentration tensor is provided and simple analytical formula are proposed and compared for different homogenization schemes. A combination of these results with acoustic emission data allows the identification of the parameters involved in the local failure criterion. It has been shown that the predicted interfacial strength highly depends on the choice of a suitable homogenization scheme.     

Mixed mode ductile fracture using the strain energy density criterion

An investigation of extending the application of the strain energy density criterion to mixed mode ductile fracture is described. Thin plates embedded with a center crack inclined at =30 and 60 degrees are analysed. An Euclerian finite element formulation is used for the large elastic-plastic flow problem incorporating isotropically hardening Prandtl-Reuss material and incremental deformation.An alternative criterion based on the maximum dilatational energy for determining crack initiation angle in ductile fracture is proposed. Based on this criterion, the predicted fracture loads for the cracked plates of =30 and 60 degrees are compared satisfactorily with the measurements.     

Prediction of ductile fracture initiation using micromechanical analysis

In the paper ductile fracture initiation analysis of low-alloyed ferritic steel has been made by application of two micromechanical models: the Rice–Tracey void growth model and the Gurson–Tvergaard–Needleman (GTN) model. The aim of the study was to analyse transferability of micromechanical parameters determined on specimens without initial crack to pre-cracked specimens. A significant part of the research has been carried out through participation in the round robin project organised by the European Structural Integrity Society (ESIS). Tensile tests have been performed on cylindrical smooth specimens and CT specimens. Critical values of micromechanical parameters determined on smooth specimen for both applied models, have been used for prediction of the crack growth initiation in CT specimen. Modelling of the first phase of ductile fracture––void nucleation––has been carried out using quantitative metallographic analysis of non-metallic inclusion content in tested steel. For determination of critical values of model parameters corresponding to ductile fracture initiation a simple procedure has been applied based on a combination of experimental and numerical results. Evaluated J-integral values corresponding to onset of crack growth, J_i, are in good agreement with experimental result and both models have proved to be suitable for determination of the ductile fracture initiation in tested steel. The effect of FE size at a crack tip on J_i-value has been particularly analysed: it has been established that the calculation with FE size corresponding to the mean free path λ between inclusions in steel gives results that are in accordance with the experimental ones.     

基于Oyane韧性断裂准则的板料成形极限预测

本文基于Oyane韧性断裂准则,结合数值模拟方法,预测板料不同应变状态下的极限应变.准则中的材料参数通过单向拉伸和平面应变拉伸试验确定.在模拟胀形试验获得每一时间步应力、应变值的基础上,应用韧性断裂准则预测板料的成形极限.模拟结果表明用韧性断裂准则和数值模拟相结合的方法能成功获得板料的成形极限图.     

Prediction of crack initiation and propagation of adhesive lap joints using an energy failure criterion

In a previous paper, the present authors have pointed out limitations of some fracture mechanics parameters and shown that the vectorial J-integral can be applied to adhesive joints. Here, problems concerning the practical application of the vectorial J-integral are discussed and a more suitable failure criterion has been proposed, based on a specific strain energy criterion. The specific energy is not so sensitive to the size of the integration zone since it is ‘averaged’ over the volume of the zone. This criterion has been used to model the crack initiation and propagation in single lap joints with a brittle adhesive and a ductile adhesive. The effect of the shrinkage thermal stresses, adhesive fillet, surface preparation and type of adherends (aluminium and steel) were studied. The predicted failure loads and crack patterns are in very good agreement with the experimental results. One of the major conclusions is that the predictions can explain well the experimental scatter band that is always present in single lap joints due to the difficulty of controlling the adhesive fillet.     

Damage work as ductile fracture criterion

This paper treats the ductile failure initiation in circumferentially-notched tension specimens and explores the local damage model that is able to represent the continuous degradation of the deforming material. With the aid of finite element calculations, the notched specimens have been simulated numerically and the whole strain-stress history for each geometry derived. This allows determination of the evolution of strain-stress fields until fracture occurs. Two damage models were evaluated: the Rice and Tracey cavity growth model and a model which combines the latter with the plastic strain work, to derive an intrinsic parameter called damage work. These models could predict the location where the crack will initiate as well as the crack initiation step which is reached for a relatively constant value of the critical damage.     

Fast failure prediction of adhesively bonded structures using a coupled stress‐energetic failure criterion

The use of adhesively bonded joints in industrial structures requires reliable tools for the estimation of the failure load. The necessary and sufficient condition to predict the strength of such joints involves the implementation of a coupled stress and energetic criteria. However, its application necessitates the identification of the stress distribution along the adhesive layer, which has been approximated in this paper by a previously published closed‐form solution. This analysis along with finite element modelling results are compared with experimental data issued from a double‐notched sample tested with the Arcan fixture at various load ratios. The results show good agreement; the use of the closed‐form solution permitted to predict the failure load more rapidly and in a conservative manner compared with the experimental results. The application of the methodology is also extended to a wider range of joint geometries by means of spatial interpolation using the Kriging model.     

一种韧性断裂模型的理论研究和实验验证

为研究高强钢板成形过程中的损伤破裂机理,更准确地预测高强钢的断裂失效行为,基于细观损伤力学的空穴理论,并在屈服函数就是塑性势函数的通用性假设基础上推导了各向同性的韧性断裂模型;同时引入Lode参数以反映不同应变状态下空穴形核、长大以及聚合的差异,提出了一种包含应力三轴度和Lode参数的新模型.在Hill正交各向异性屈服假设下,描述了平面应力状态下应力比值、r值与应力三轴度、等效塑性应变的关系.最后,针对DP590进行了参数确定和实验验证.结果表明:应力三轴度在高强钢韧性断裂中仍然起主导因素,在低应力三轴下,材料主要是剪切型破坏,空穴的长大及聚合方式主要受剪应力影响,高应力三轴下,空穴损伤主要受拉应力影响,断裂是韧窝形的;Lode参数决定了应力组成形式,也间接地反映了应变状态,它与应力三轴度共同决定了空穴损伤的发展.新的模型能较准确地预测DP590的成形极限.