Analysis of ductile to cleavage transition in part-through cracks using a cell model incorporating statistics

This paper describes an approach to study ductile/cleavage transition in ferritic steels using the methodology of a cell model for ductile tearing incorporating weakest link statistics. The model takes into account the constraint effects and puts no restriction on the extent of plastic deformation or amount of ductile tearing preceding cleavage failure. The parameters associated with the statistical model are calibrated using experimental cleavage fracture toughness data, and the effect of threshold stress on predicted cleavage fracture probability is investigated. The issue of two approaches to compute Weibull stress, the 'history approach' and the 'current approach', is also addressed. The numerical approach is finally applied to surface-cracked thick plates subject to different histories of bending and tension, and a new parameter, ψ, is introduced to predict the location of cleavage initiation.     

6.5%Si高硅钢铸锭凝固组织的CAFE法模拟研究

应用CAFE法对6.5%Si高硅钢铸锭凝固组织进行了模拟研究,确定出了适合高硅钢组织模拟的模型。进一步用该模型研究了过热度及冷却条件对凝固组织的影响,结果表明,随着过热度的降低,凝固组织中柱状晶比例和晶粒平均面积均减小。水冷条件下,高硅钢铸锭凝固组织几乎全是柱状晶,而且晶粒粗大。空冷条件下,等轴晶区扩大,但柱状晶仍占主要部分。缓冷条件下,等轴晶区占主要部分,晶粒平均面积和空冷条件下相当。     

锈蚀钢框架地震损伤模型研究

为了合理地描述锈蚀钢框架的地震破坏形式及不同程度的锈蚀对钢框架抗震性能的影响,在欧进萍等人提出的钢结构地震损伤模型的基础上建立锈蚀钢结构地震损伤模型。为确定锈蚀钢结构地震损伤模型参数,分别给出锈蚀梁、柱构件双线性恢复力模型特征点的计算方法,并通过弹塑性时程分析获得损伤模型中的其他参数数值。利用加权系数法合理地考虑锈蚀构件损伤向整体结构损伤迁移转化的多尺度效应,建立锈蚀钢框架整体地震损伤模型。结合该损伤模型的特点,定义了对应结构不同破坏等级的损伤指数范围。最后,对5榀具有不同锈蚀率的平面钢框架结构进行了弹塑性时程分析,结果表明:所建的损伤模型能在一定程度上反映钢框架结构随锈蚀程度的退化规律。     

Equivalent localization element for crack band approach to mesh‐sensitivity in microplane model

The paper presents in detail a novel method for finite element analysis of materials undergoing strain‐softening damage based on the crack band concept. The method allows applying complex material models, such as the microplane model for concrete or rock, in finite element calculations with variable finite element sizes not smaller than the localized crack band width (corresponding to the material characteristic length). The method uses special localization elements in which a zone of characteristic size, undergoing strain softening, is coupled with layers (called ‘springs’) which undergo elastic unloading and are normal to the principal stress directions. Because of the coupling of strain‐softening zone with elastic layers, the computations of the microplane model need to be iterated in each finite element in each load step, which increases the computer time. Insensitivity of the proposed method to mesh size is demonstrated by numerical examples. Simulation of various experimental results is shown to give good agreement. Copyright © 2004 John Wiley & Sons, Ltd.     

基于应变和比能双控的钢结构损伤模型

损伤模型是对经历地震后结构的剩余承载力进行定量评价的重要工具。本文提出了一个基于等效塑性应变和比能双控的损伤模型,从材料的角度出发,考虑了三轴应力对地震作用下结构性能的影响,可用于空间结构强震作用下的非线性分析。应用该模型对一个九层的benchmark结构进行了地震倒塌模拟分析,结果显示基于应变与比能双控的损伤模型能够很好地评估强震下钢结构竖向构件及层的损伤发展过程。     

Ductile damage modelling with locking‐free regularised GTN model

The major goal of this work is to develop a robust modelling strategy for the simulation of ductile damage development including crack initiation and subsequent propagation. For that purpose, a Gurson‐type model is used. This model class, as many other damage models, leads to significant material softening and must be used within a large deformation framework due to the ductile character of the materials. This leads to 2 main difficulties that should be dealt with carefully: mesh dependency and volumetric locking. In this work, a logarithmic finite strain framework is adopted in which the Gurson‐Tvergaard‐Needleman constitutive law is reformulated. Then a nonlocal formulation with regularisation of hardening variable is applied so as to solve mesh dependency and strain localization problem. In addition, the nonlocal model is combined with mixed “displacement‐pressure‐volume variation” elements to avoid volumetric locking. Thereby, a mesh‐independent and locking‐free finite strain framework suitable for the modelling of ductile rupture is established. Attention is paid to mathematical properties and numerical performance of the model. Finally, the model parameters are identified on an experimental database for a nuclear piping steel. Simulations of standard test specimens (notched tensile bars and compact tension and single edge notched tensile cracked specimens) are performed and compared to experimental results.     

Finite element formulation of the Ogden material model with application to rubber-like shells

The present contribution proposes a variational procedure for the numerical implementation of the Ogden material model. For this purpose the strain energy density originally formulated in terms of the principal stretches is transformed as variational quantities into the invariants of the right Cauchy–Green tensor. This formulation holds for arbitrary three-dimensional deformations and requires neither solving eigenvalue problems nor co-ordinate system transformations. Particular attention is given to the consideration of special cases with coinciding eigenvalues. For the analysis of rubber-like shells this material model is then coupled with a six parametric shells kinematics able to deal with large strains and finite rotations. The incompressibility condition is considered in the strain energy, but it is additionally used as 2-D constraint for the elimination of the stretching parameter at the element level. A four node isoparametric finite element is developed by interpolating the transverse shear strains according to assumed strain concept. Finally, examples are given permitting to discuss the capability of the finite element model developed concerning various aspects. © 1998 John Wiley & Sons, Ltd.     

A statistical model for cleavage fracture in notched specimens of C–Mn steel

A statistical model for cleavage fracture in notched specimens of C-Mn steel has been proposed. This model is based on a recently suggested physical model. This statistical model satisfactorily describes the distributions of the cumulative failure probability and failure probability density of 36 notched specimens fractured at various loads at test temperature of −196 °C. The minimum notch toughness has also been discussed.     

Ductile tearing analyses of cracked TP304 pipes using the multiaxial fracture strain energy model and the Gurson–Tvergaard–Needleman model

Ductile crack growth behaviours of TP304 pipes containing different circumferential defects were investigated in the study. Finite element (FE) damage analysis of the ductile fracture was carried out based on an uncoupled multiaxial fracture strain energy (MFSE) model with only two model parameters, which can be calibrated by data from tensile tests and fracture toughness tests. For the purpose of comparison, the Gurson–Tvergaard–Needleman (GTN) model was also employed in the FE damage analysis. It is observed that the MFSE model can reproduce the ductile tearing experiments as excellently as the GTN model does. Despite its simplicity, the MFSE model can reasonably predict the magnitudes of the crack initiation load and maximum load, the load‐line displacement, the crack mouth opening displacement, the crack extension and the crack profiles in the full‐scale cracked pipe tests.     

混凝土弹塑性损伤帽盖模型参数确定研究

摘要:基于连续损伤力学和塑性力学理论形成的弹塑性损伤帽盖模型是一个高级混凝土本构关系模型,但模型涉及的参数过多却给运用造成了不便。本文对模型参数进行详细解释基础上,采用已有的混凝土材料试验数据给出了其子午线强度参数、帽盖参数、脆性损伤和延性损伤参数取值,大大方便了工程运用。最后以单轴拉伸和单轴压缩为例数值演示了模型基本力学特性。     

Aspects of ductile failure prediction of interstitial-free steel based on a Gurson-type damage model

Numerical simulation of manufacturing processes has been gaining widespread attention owing to importance in the development of new products and components. In a parallel path, there has been a substantial development of steels with improved mechanical characteristics, such as the interstitial-free (IF) steel. The present work is inserted within this context and introduces application of a micromechanical modelling approach to an interstitial-free steel based on a Gurson-type constitutive model with the objective of assessing the evolution of mechanical degradation and failure prediction in fracture-free materials. The inelastic material parameters were obtained from tensile tests of cylindrical specimens. Evolution of the mechanical degradation, represented by a micromechanical damage measure, is discussed based on three-point bend tests.     

Use of a modified Gurson model for the failure behaviour of the clinched joint on Al6061 sheet

This paper discusses the ductile fracture behaviour of the clinched joint on Alloy 6061 sheets. Failure behaviour of the clinched joint is associated with the nucleation, growth and coalescence of voids within the microstructure. Various corrections to the original Gurson model are proposed to allow for instability and final fracture of the material. This paper is concerned with the application of the modified Gurson–Tvergaard–Needleman damage developed by Ken Nahshon and Zhenyu Xue. The results of the tension tests are compared with those of numerical analysis to obtain the initial void volume fraction f₀ and the shear damage coefficients k_w. The modified Gurson–Tvergaard–Needleman model is used to describe the failure behaviour and the shear strength of the clinched joint. Good agreement is shown between the experiment results and the numerical results on the location of fracture and the maximum failure load.     

A micro‐mechanical damage model based on gradient plasticity: algorithms and applications

As soon as material failure dominates a deformation process, the material increasingly displays strain softening and the finite element computation is significantly affected by the element size. Without remedying this effect in the constitutive model one cannot hope for a reliable prediction of the ductile material failure process. In the present paper, a micro‐mechanical damage model coupled to gradient‐dependent plasticity theory is presented and its finite element algorithm is discussed. By incorporating the Laplacian of plastic strain into the damage constitutive relationship, the known mesh‐dependence is overcome and computational results are uniquely correlated with the given material parameters. The implicit C¹ shape function is used and can be transformed to arbitrary quadrilateral elements. The introduced intrinsic material length parameter is able to predict size effects in material failure. Copyright © 2002 John Wiley & Sons, Ltd.     

Numerical implementation and analysis of a class of metal plasticity models coupled with ductile damage

This paper deals with a class of rate-independent metal plasticity models which exhibit non-linear isotropic hardening, non-linear kinematic hardening (Chaboche-Marquis model) and ductile damage (Lemaitre-Chaboche model). The backward Euler scheme is used to integrate the rate constitutive relations. The non-linear equations obtained are solved by the Newton method. The consistent tangent operator is obtained by exact linearization of the algorithm. Despite the complexity of the constitutive equations, closed-form expressions are derived, without any approximations. Analytical, numerical and experimental results are presented and discussed.     

Combined continuum damage‐embedded discontinuity model for explicit dynamic fracture analyses of quasi‐brittle materials

In this paper, a novel constitutive model combining continuum damage with embedded discontinuity is developed for explicit dynamic analyses of quasi‐brittle failure phenomena. The model is capable of describing the rate‐dependent behavior in dynamics and the three phases in failure of quasi‐brittle materials. The first phase is always linear elastic, followed by the second phase corresponding to fracture‐process zone creation, represented with rate‐dependent continuum damage with isotropic hardening formulated by utilizing consistency approach. The third and final phase, involving nonlinear softening, is formulated by using an embedded displacement discontinuity model with constant displacement jumps both in normal and tangential directions. The proposed model is capable of describing the rate‐dependent ductile to brittle transition typical of cohesive materials (e.g., rocks and ice). The model is implemented in the finite element setting by using the CST elements. The displacement jump vector is solved for implicitly at the local (finite element) level along with a viscoplastic return mapping algorithm, whereas the global equations of motion are solved with explicit time‐stepping scheme. The model performance is illustrated by several numerical simulations, including both material point and structural tests. The final validation example concerns the dynamic Brazilian disc test on rock material under plane stress assumption. Copyright © 2014 John Wiley & Sons, Ltd.     

Modelling the pressure die casting process using a hybrid Finite‐Boundary Element model

In this paper an efficient three‐dimensional hybrid thermal model for the pressure die casting process is described. The Finite Element Method (FEM) is used for modelling heat transfer in the casting, and the Boundary Element Method (BEM) for the die. The FEM can efficiently account for the non‐linearity introduced by the release of latent heat on solidification, whereas the BEM is ideally suited for modelling linear heat conduction in the die, as surface temperatures are of principal importance. The FE formulation for the casting is based on the modified effective capacitance method, which provides high accuracy and unconditional stability. This is essential for accurate modelling of the pressure die casting process and efficient coupling to the BEM. The BE model caters for surface phenomena such as boiling in the cooling channels, which is important, as this effectively controls the manner in which energy is extracted. The die temperature is decomposed into two components, one a steady‐state part and the other a time‐dependent perturbation. This approach enables the transient die temperatures to be calculated in an efficient way, since only die surfaces close to the die cavity are considered in the perturbation analysis. A multiplicative Schwarz method for non‐overlapping domains is used to couple the individual die blocks and casting. The method adopted makes use of the weak coupling between the domains, which is a result of the relatively high interfacial thermal resistance that is present. Numerical experiments are performed to demonstrate the computational effectiveness of the approach. Predicted die and casting temperatures are compared with thermocouple measurements and good agreement is indicated. Copyright © 1999 John Wiley & Sons, Ltd.     

Extension of the modified Bai‐Wierzbicki model for predicting ductile fracture under complex loading conditions

The ductile fracture behaviour of metallic materials is strongly dependent on the material's stress state and loading history. This paper presents a concept of damage initiation and failure indicators and corresponding evolution laws to enhance the modified Bai‐Wierzbicki model for predicting ductile damage under complex loading conditions. The proposed model considers the influence of stress triaxiality and the Lode angle parameter on both damage initiation and the subsequent damage propagation. The model parameters are calibrated for C45E + N steel using a series of mechanical tests and numerical simulations. The enhanced approach is applied to the modelling of various mechanical tests under proportional and non‐proportional loading conditions and successfully predicts the ductile damage behaviour in these tests.     

基于CAFE法模拟自然对流对微观组织的影响

在分析元胞自动机-有限元(CAFE)法模拟凝固过程微观组织物理本质和数值计算方法的基础上,运用该法模拟了对流对凝固过程中的温度场、缩孔和疏松及微观组织的影响。模拟结果表明:该法可以实现铸件三维微观组织的模拟,模拟结果与实验吻合较好。对流可以起到均匀温度场的作用;对流对凝固过程中的补缩有一定的影响,使缩孔、疏松形貌不规则;对流可以细化铸件的微观组织。