Conditions of the ductile-brittle transition in failure of polymer materials

Conclusions The polymer materials are characterized by the transition from ductile to brittle fracture with increasing loading rate and decreasing temperature. The brittle fracture susceptibility of the material can be determined on the basis of the critical size of the defect/ crack. The measure of the cracking resistance of plastics can often be represented by the material scale of the crack length. The quality of the critical size of the defect/crack to the material scale of the crack length can be used as a criterion determining the conditions of transition from ductile to brittle fracture.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 779–785, September–October, 1988.     

A Phase Field Model for Ductile to Brittle Failure Mode Transition

The computational modeling of failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in dynamic problems with complex crack topologies. This can be overcome by a diffusive crack modeling based on the introduction of a crack phase field. We outline a conceptual framework for phase field models of crack propagation in brittle elastic and ductile elastic-plastic solids under dynamic loading and investigate the ductile to brittle failure mode transition observed in the experiment performed by Kalthoff and Winkeler [3]. We develop incremental variational principles and consider their numerical implementations by multi-field finite element methods. To this end, we define energy storage and dissipation functions for the plastic flow including the fracture phase field. The introduction of local history fields that drive the evolution of the crack phase field inspires the construction of robust operator split schemes. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

韧脆转变的一种细观随机模糊统计分析

对不同温度和应力状态下40Cr材料进行大子样宏观试验和细观观测,提出了一种新的材料断裂韧脆转变统计随机模糊模型。该模型认为,在统计意义上,材料的韧性断裂为空穴机制,临界空穴扩张比参数可以作为韧性断裂的判据;材料的脆性断裂可以用内嵌币状裂纹的脆性断裂模型来模拟,为此测量断裂特征长度,提出并具体计算了控制币状裂纹失稳扩张的细观临界应力强度因子;在韧脆转变区域内,这两种机理并存并相互竞争,为此提出了模糊准则。对模型参数进行了测量和统计分析,给出分布规律,给出了计算断裂特征的概率模型。计算了韧脆转变区域内的细观机制变化和宏观响应。结果表明,该模型及分析方法可以很好地模拟应力状态及温度对韧脆转变的影响。     

Phase Field Modeling of Brittle and Ductile Fracture

The phase field modeling of brittle fracture was a topic of intense research in the last few years and is now well-established. We refer to the work [1-3], where a thermodynamically consistent framework was developed. The main advantage is that the phase-field-type diffusive crack approach is a smooth continuum formulation which avoids the modeling of discontinuities and can be implemented in a straightforward manner by multi-field finite element methods. Therefore complex crack patterns including branching can be resolved easily. In this paper, we extend the recently outlined phase field model of brittle crack propagation [1-3] towards the analysis of ductile fracture in elastic-plastic solids. In particular, we propose a formulation that is able to predict the brittle-to-ductile failure mode transition under dynamic loading that was first observed in experiments by Kalthoff and Winkler [4]. To this end, we outline a new thermodynamically consistent framework for phase field models of crack propagation in ductile elastic-plastic solids under dynamic loading, develop an incremental variational principle and consider its robust numerical implementation by a multi-field finite element method. The performance of the proposed phase field formulation of fracture is demonstrated by means of the numerical simulation of the classical Kalthoff-Winkler experiment that shows the dynamic failure mode transition. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The diffraction of elastic waves by an imperfect fusion bond

We consider diffraction by a semi-infinite crack located alonga fusion interface between two differing elastic media. Twotypes of crack, namely open and partially closed cracks, areinvestigated. An open crack is modelled by a stress-free contactboundary condition and a partially closed crack is modelledby a spring contact boundary condition. For the latter, thejump in the stress across the crack is assumed to be proportionalto the jump in the displacement across the crack. This situationarises in, for example, a K-weld where the fine grain of theparent material (for example, ferritic or forged austeniticsteel) is in stark contrast with the coarse-grained weld metal(for example, austenitic weld metal). In the metal weld thedirection of the grain axis varies through the metal. However,diffraction is a local phenomenon and so the austenitic steelis assumed to have a zonal axis so that it may be modelled bya transversely isotropic composite. The ferritic or forged austeniticsteel will be modelled as an isotropic material.     

Modelling thermoplastic material behaviour of dual-phase steels on a microscopic length scale

On a microscopic length scale dual-phase steels exhibit a polycrystalline microstructure consisting of ferrite and martensite. In this work a material model for the temperature dependent hardening behaviour of the ferritic phase is presented. As the dislocation structure determines the resistance to dislocation glide, dislocation densities are introduced as state variables to capture the dependence of the material behaviour on the loading history. Motivated by the elementary processes of multiplication by the Frank-Read-mechanism and annihilation by cross-slip, evolution equations for the dislocation densities are introduced. Based on the interaction of dislocations on different slip systems and the Peierls-stress, the resistance to dislocation motion with its temperature dependence is formulated to describe the hardening behaviour. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling thermoplastic material behaviour of dual-phase steels on a microscopic length scale - numerical treatment

On a microscopic length scale dual-phase steels exhibit a polycrystalline microstructure consisting of ferrite and martensite. In this work it is assumed that the martensitic phase behaves purely thermoelastic while for the ferritic phase a thermoplastic material model was developed based on the assumption that the driving mechanism for persistent deformation is the movement of dislocations on preferred planes in preferred directions. The necessary shear stress to move dislocations at a certain temperature and deformation rate is assumed to possess contributions from the atomic lattice, alloying atoms and the dislocation structure. To consider the influence of the dislocation structure, dislocation densities are introduced as state variables for which temperature and deformation rate dependent evolution equations are formulated. Since for general loading histories the model equations cannot be integrated analytically, a time discretized form of the model equations with an appropriate solution algorithm is presented. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An interface crack moving between magnetoelectroelastic and functionally graded elastic layers

A constant crack moving along the interface of magnetoelectroelastic and functionally graded elastic layers under anti-plane shear and in-plane electric and magnetic loading is investigated by the integral transform method. Fourier transforms are applied to reduce the mixed boundary value problem of the crack to dual integral equations, which are expressed in terms of Fredholm integral equations of the second kind. The singular stress, electric displacement and magnetic induction near the crack tip are obtained asymptotically and the corresponding field intensity factors are defined. Numerical results show that the stress intensity factors are influenced by the crack moving velocity, the material properties, the functionally graded parameter and the geometric size ratios. The propagation of the moving crack may bring about crack kinking, depending on the crack moving velocity and the material properties across the interface.     

Ductile failure with gradient plasticity coupled to the phase-field fracture at finite strains

Most metals fail in a ductile fashion, i.e, fracture is preceded by significant plastic deformation. The modeling of failure in ductile metals must account for complex phenomena at micro-scale, such as nucleation, growth and coalescence of micro-voids. In this work, we start with von-Mises plasticity model without considering void generation. The modeling of macroscopic cracks can be achieved in a convenient way by the continuum phase field approaches to fracture, which are based on the regularization of sharp crack discontinuities [1]. This avoids the use of complex discretization methods for crack discontinuities and can account for complex crack patterns. The key aspect of this work is the extension of the energetic and the stress-based phase field driving force function in brittle fracture to account for a coupled elasto-plastic response in line with our recent work [3]. We develop a new theoretical and computational framework for the phase field modeling of ductile fracture in elastic-plastic solids. To account for large strains, the constitutive model is constructed in the logarithmic strain space, which simplify the model equations and results in a formulation similar to small strains. We demonstrate the modeling capabilities and algorithmic performance of the proposed formulation by representative simulations of ductile failure mechanisms in metals. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigation of the local behavior of different cohesive zone models

Cohesive interface elements are well suited for three-dimensional crack propagation analyses as long as the crack path is known. This is the case e.g. in delamination analyses of laminated composite structures or failure analyses of adhesively bonded joints. Actually, they are widely used in such applications for both brittle and ductile systems. As long as the strength and fracture toughness of the material are accurately captured it is generally accepted that the shape of the cohesive law has little to no influence on the mechanical behavior of the investigated structures. However, when having a look on the local behavior of different cohesive zone models, such as stress distribution in the fracture process zone, the results exhibit certain differences. These will be studied in the present contribution. Especially the local stress distribution will be investigated and the effect on the computational efficiency will be pointed out. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic crack propagation in a 2D elastic body: The out-of-plane case

Already in 1920 Griffith has formulated an energy balance criterion for quasistatic crack propagation in brittle elastic materials. Nowadays, a generalized energy balance law is used in mechanics [F. Erdogan, Crack propagation theories, in: H. Liebowitz (Ed.), Fracture, vol. 2, Academic Press, New York, 1968, pp. 498-586; L.B. Freund, Dynamic Fracture Mechanics, Cambridge Univ. Press, Cambridge, 1990; D. Gross, Bruchmechanik, Springer-Verlag, Berlin, 1996] in order to predict how a running crack will grow. We discuss this situation in a rigorous mathematical way for the out-of-plane state. This model is described by two coupled equations in the reference configuration: a two-dimensional scalar wave equation for the displacement fields in a cracked bounded domain and an ordinary differential equation for the crack position derived from the energy balance law. We handle both equations separately, assuming at first that the crack position is known. Then the weak and strong solvability of the wave equation will be studied and the crack tip singularities will be derived under the assumption that the crack is straight and moves tangentially. Using the energy balance law and the crack tip behavior of the displacement fields we finally arrive at an ordinary differential equation for the motion of the crack tip.     

论复合型脆断的周向应变因子准则

本文讨论了线弹性断裂力学的复合型断裂准则.推荐了周向应变因子准则.     

In-situ study of martensitic transformation and nucleation, propagation of crack in CuNiAl shape memory alloy

The stress-induced martensitic transformation and its relation with crack nucleation and propagation in CuNiAl shape memory alloy were investigated through in-situ tensile tests by SEM and TEM. The results indicated that the stress concentration ahead of the crack tip could induce formation of stacking faults and different types of martensites. TEM observations showed that the martensites could transform from one type to another and even reversely to the parent during loading. The microcracks nucleated along the martensite/parent interface and intersection between two martensites. When the crack propagated a certain distance, the stress concentration ahead of the crack tip was large enough to result in formation of slip bands, and in this condition the microcrack nucleated along slip bands more easily.     

带复合型摩擦裂纹的圆盘动态断裂实验有限元分析

为验证考虑裂纹面接触和动态荷载时,中心裂纹巴西圆盘（CCBD）试件用于分离式Hopkinson压杆（SHPB）系统中测量脆性材料复合型动态断裂韧度的可行性,以及研究裂纹面接触对动态断裂韧度实验结果的影响.通过有限元法建立SHPB CCBD三维有限元模型,计算了不同加载条件下CCBD试件的动态应力强度因子（DSIF）.结果表明:在实验中,将考虑裂纹面接触的应力强度因子(SIF)准静态公式推广为动态公式,需要判定断裂时间是否达到应力平衡的时间条件;压剪复合型加载时,裂纹面接触导致裂纹面应力变化,会对Ⅱ型裂纹的DSIF产生显著影响,不考虑裂纹面接触的影响将会导致Ⅱ型DSIF的测试值偏大.     

Prediction of fracture toughness of embrittled steels by means of the Small Punch Test

To characterise the randomly distributed strength and fracture toughness of brittle steels, many specimens have to be destroyed. Since the Small Punch Test (SPT) needs only little material, it is a well suited experiment, when only a small volume of material is available. In this study the cleavage fracture of a ferritic steel at low temperature was investigated using the Beremin model. The failure probability is described with a 2-parameter Weibull distribution in terms of the so-called Weibull stress, which is calculated using an elastic-plastic finite element stress analysis. While the transfer of Weibull parameters works well between similar geometries and loading conditions, it works bad in more general cases. Modifications of the Beremin model are necessary to overcome this problem. Recent publications consider a lower threshold value of the Weibull stress, which leads to a lower Weibull modulus and therefore to a stronger volume size effect of strength. The suitability of this approach to transfer cleavage fracture results from SPT to fracture mechanics specimens was investigated. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Study on the dynamics of the double cantilever-beam specimen of decagonal Al-Ni-Co quasicrystals

This paper investigated dynamic initiation of crack growth and crack fast propagation for the double cantilever-beam specimen (DCB) of two-dimensional decagonal Al-Ni-Co quasicrystals. The elasto-/hydro-dynamic model for wave propagation and diffusion together with their interaction is adopted. Numerical results of stresses, displacements and dynamic stress intensity factor are obtained by the finite difference method. Dynamic initiation of crack growth and crack fast propagation are discussed in detail in which the latter is a nonlinear problem arising from moving boundary effect, which is in particular explored.     

Deformation induced martensite transformation in a cold-worked forming process of austenitic stainless steel

Within the last years the goal of industrial manufacturing processes – such as tube forming – has shifted towards an optimization of technological as well as mechanical properties of the manufactured structures. For example, during the forming procedure of sheets made of austenitic stainless steel X5CrNi18-10, the content of strain-induced martensite needs to be controlled. In order to achieve optimal structural properties of the manufactured tube with respect to very high-cycle fatigue (VHCF), a martensite ratio of approximately 25% needs to be obtained [1]. On the basis of experimental investigations this contribution deals with the numerical simulation of the tube-forming process with special consideration of the martensite ratio c as a function of temperature and deformation field. For this purpose we extend an existing martensite model on polyaxial states of stress and compare experimental results and numerical simulations for the modified model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An enhanced model for probabilistic cleavage fracture assessment considering local constraint effects

The present study is concerned with the development of an enhanced probabilistic model for cleavage assessment of ferritic steels. An enhanced model for the probabilistic cleavage fracture assessment has to consider the conditions for both, nucleation and propagation of micro defects. Hence, a propagation based model is enhanced by a combination of the local plastic strain and the local stress triaxiality to account for the nucleation of potentially critical micro defects. The formulation of the new model is based on the local mechanical field quantities determined numerically at the cleavage origins for a variety of standard deep and shallow crack specimens as well as for small scale cruciform bending specimens. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)