A Phase Field Approach for Dynamic Fracture

In phase field fracture models cracks are indicated by the value of a scalar field variable which interpolates smoothly between broken and undamaged material. The evolution equation for this crack field is coupled to the mechanical field equations in order to model the mutual interaction between the crack evolution and mechanical quantities. In finite element simulations of crack growth at comparatively slow loading velocities, a quasi-static phase field model yields reasonable results. However, the simulation of fast loading or the nucleation of new cracks challenges the limits of such a formulation. Here, the quasi-static phase field model predicts brutal crack extension with an artificially high crack speed. In this work, we analyze to which extend a dynamic formulation of the mechanical part of the phase field model can overcome this paradox created by the quasi-static formulation. In finite element simulations, the impact of the dynamic effects is studied, and differences between the crack propagation behavior of the quasi-static model and the dynamic formulation are highlighted. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

各向异性材料动态裂纹扩展特性和动态应力强度因子

基于各向异性材料力学,研究了无限大各向异性材料中Ⅲ型裂纹的动态扩展问题．裂纹尖端的应力和位移被表示为解析函数的形式,解析函数可以表达为幂级数的形式,幂级数的系数由边界条件确定．确定了Ⅲ型裂纹的动态应力强度因子的表达式,得到了裂纹尖端的应力分量、应变分量和位移分量．裂纹扩展特性由裂纹扩展速度M和参数alpha反映,裂纹扩展越快,裂纹尖端的应力分量和位移分量越大;参数alpha对裂纹尖端的应力分量和位移分量有重要影响．     

Inclusion Size Distribution and Endurance Limit of a Hard Steel

High cycle fatigue failure of hard steels is dominated by a long crack initiation phase and a short crack propagation phase. The crack initiation sites are inclusions or surface defects. Due to this, the endurace probability of a hard steel part depends on its crack initiating inclusion size or surface defect size distribution. These consideration lead to the weakest-link concept which allows to calculate local and total endurance probabilities of the cycled parts. From these probabilities, the endurance limit and the probable crack initiation sites can be predicted. Base of the prediction is the knowledge of the endurance limits under three different load conditions. From these data and fracture-mechanic relations for the different inclusion types, the distributions of the crack initiating inclusion sizes can be predicted.     

Theoretical and experimental investigation of bone fracture in the human proximal femur

Proximal femur fractures are very common injuries especially among older patients. Although, there are various alternatives and improvements in implant design and operating techniques, the treatment still represents a big medical challenge. Therefore, the understanding of crack initiation and propagation in the proximal femur is of great interest. The objective of this work is to present a simplified phenomenological model that is able to predict crack initiation and propagation in the proximal femur. This will be simulated by using a phase-field modelling (PFM) approach. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Probabilistic modeling and simulation of multiple surface crack propagation and coalescence

In the low cycle fatigue (LCF) regime, fatigue failure of metallic materials with high strength and less impurities generally dominates by multiple surface crack propagation and coalescence, in which its final failure shows a stochastic nature on crack initiation, propagation and coalescence under cyclic loadings. According to this, the competing failure modes of multiple surface cracks and interior cracks are studied through coupling numerical simulations with fracture mechanics methods. In particular, a probabilistic procedure for modeling multiple surface crack propagation and coalescence is established by incorporating Monte Carlo simulation with experimental evidences, including surface crack density and crack length distributions measured from LCF replica tests of 30NiCrMoV12 steel. In addition, it calculates the probability of coalescence of neighboring cracks with allowance for their interactions and local plastic deformation at the crack tips. Finally, it estimates the remaining usage lives of specimens from initial state to critical cracks by propagation and coalescence of dispersed cracks.     

An experimental and computational investigation of crack initiation and stable crack growth of ductile materials

Crack initiation and stable crack growth under monotonic loading in steels has been studied using an elastic-plastic finite element analysis. The fracture criterion used for crack initiation and stable crack growth was the critical strain energy density. In addition the shift core method for the analysis of crack extension was used. In the shift core modelling method, crack advance is simulated by moving the coordinates of the core region which surrounds the crack tip, to obtain the stiffness reduction. Simultaneously the core itself geometrically undergoes a simple rigid-body motion or translation during the crack extension. The analytically calculated and experimentally measured load for crack initiation and the subsequent stable crack growth agreed well.     

PROCRACK-A Software Tool for Finite Element Simulation of Three-Dimensional Fatigue Crack Growth

The lifetime of structural components is limited by fatigue cracks. After initiation from an existing defect the crack grows subcritically until it reaches a critical size. At this point it becomes unstable and the structural component fails. PROCRACK is a powerful tool that enables the commercial finite element software Abaqus to calculate the crack propagation in pre-cracked components. The complete capability of Abaqus can be used to simulate nearly arbitrary geometries. Abaqus/CAE is used for the three-dimensional modeling of the initial crack at a geometrical level by means of points, lines and triangles. The numerical analysis is performed by Abaqus/Standard. PROCRACK automatically generates a tube-shaped submodel around the crack front to calculate the stress intensity factors with high accuracy. The Paris law or the NASGRO equation can be used to calculate the incremental crack growth. The shape of the crack and the finite element mesh are updated in every crack growth step. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermal Shock Crack Propagation of Alumina Simulated With the Phase-Field Method Under Temperature-Dependent Damage Criteria北大核心CSCD

氧化铝陶瓷材料的力学性能受温度影响显著,因此使用相场法模拟热冲击裂纹的扩展时有必要考虑损伤判据的温度相关性.在现有热力学相场模型的基础上通过引入温度相关性损伤判据,修正了相场模型的控制方程.利用该模型对氧化铝陶瓷热冲击实验进行有限元模拟,并将模拟结果与氧化铝热冲击实验结果和不考虑温度相关性损伤判据的有限元模拟结果进行对比.结果表明,通过引入温度相关性损伤判据,可实现对热冲击裂纹的萌生和扩展过程更合理的模拟.     

非线性断裂动力学中的路径无关积分和断裂准则

本文考虑非线性断裂动力学中的路径无关积分和断裂准则.在讨论中计入了动力效应和裂纹的传播现象,考虑了裂纹在非线性弹性介质中的传播以及在弹塑性介质中的传播二种情况,作出了一些相应的路径无关积分.作为例子.讨论了裂纹的定常传播情况.最后,给出了这种路径无关积分的力学意义.说明它可用来作为非线性断裂动力学的一种断裂准则.     

Simulation of short crack propagation using a hybrid boundary element technique

Service life of cyclically loaded components is often determined by the propagation of short fatigue cracks, which is highly influenced by microstructural features such as grain boundaries. A two-dimensional model to simulate the growth of such stage I-cracks is presented. The crack is discretised by dislocation discontinuity boundary elements and the direct boundary element method is used to mesh the grain boundaries. A superposition procedure couples these different boundary element methods to employ them in one model. Varying elastic properties of the grains are considered and their influence on short crack propagation is studied. A change in crack tip slide displacement determining short crack propagation is observed. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Development of a finite-element analysis methodology for the propagation of delaminations in composite structures

Analysing the collapse of skin-stiffened structures requires capturing the critical phenomenon of skin-stiffener separation, which can be considered analogous to interlaminar cracking. This paper presents the development of a numerical approach for simulating the propagation of interlaminar cracks in composite structures. A degradation methodology was introduced in MSC.Marc, which involved the modelling of a structure with shell layers connected by user-defined multiple-point constraints (MPCs). User subroutines were written that employ the virtual crack closure technique (VCCT) to determine the onset of crack growth and modify the properties of the user-defined MPCs to simulate crack propagation. Methodologies for the release of failing MPCs are presented and are discussed with reference to the VCCT assumption of self-similar crack growth. The numerical results obtained by using the release methodologies are then compared with experimental data for a double-cantilever beam specimen. Based on this comparison, recommendations for the future development of the degradation model are made, especially with reference to developing an approach for the collapse analysis of fuselage-representative structures. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 1, pp. 15–42, January–February, 2007.     

Out-of-plane displacement measurement near the crack tip during a crack propagation: Validation of a 3D formulation for a specimen in PMMA loaded in mode I.

The fundamental aim of this study is the determination zone of the 3D effects and the transient one at the vicinity of the crack tip during a crack propagation in brittle materials ( PMMA ) using an optical method (Michelson interferometer). With the obtained interferograms, we can extract the phase (thus the relief) by using a new numerical approach based on the principle of images correlation between real fringes and virtual fringes. Different dynamic tests are realized by a plate loaded in mode I under a constant loading. We compare the obtained data with the two-dimensional theory of Westergaard (plane stress hypothesis) [1]. With the divergence is established, we propose a new 3D formulation, based on a formulation employed for static crack, which takes into account 3D and transient effects. For the static cracks, the 3D effects relate to a presence of the state of three-dimensional stresses. However in dynamics, the transient effects appear and are related to the crack propagation velocity. The 3D effects and transient effects lead to results equivalent to experimental ones in terms of displacement but are completely different to results given by the two-dimensional theory near the crack tip. It is possible to quantify the zone when the plane stress hypothesis is not valid according to the crack propagation speed V. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bayesian prediction of crack growth based on a hierarchical diffusion model

A general Bayesian approach for stochastic versions of deterministic growth models is presented to provide predictions for crack propagation in an early stage of the growth process. To improve the prediction, the information of other crack growth processes is used in a hierarchical (mixed‐effects) model. Two stochastic versions of a deterministic growth model are compared. One is a nonlinear regression setup where the trajectory is assumed to be the solution of an ordinary differential equation with additive errors. The other is a diffusion model defined by a stochastic differential equation where increments have additive errors. While Bayesian prediction is known for hierarchical models based on nonlinear regression, we propose a new Bayesian prediction method for hierarchical diffusion models. Six growth models for each of the two approaches are compared with respect to their ability to predict the crack propagation in a large data example. Surprisingly, the stochastic differential equation approach has no advantage concerning the prediction compared with the nonlinear regression setup, although the diffusion model seems more appropriate for crack growth. Copyright © 2016 John Wiley & Sons, Ltd.     

Crack growth modeling via 3D automatic adaptive mesh refinement based on modified-SPR technique

In this paper, the three-dimensional automatic adaptive mesh refinement is presented in modeling the crack propagation based on the modified superconvergent patch recovery technique. The technique is developed for the mixed mode fracture analysis of different fracture specimens. The stress intensity factors are calculated at the crack tip region and the crack propagation is determined by applying a proper crack growth criterion. An automatic adaptive mesh refinement is employed on the basis of modified superconvergent patch recovery (MSPR) technique to simulate the crack growth by applying the asymptotic crack tip solution and using the collapsed quarter-point singular tetrahedral elements at the crack tip region. A-posteriori error estimator is used based on the Zienkiewicz–Zhu method to estimate the error of fracture parameters and predict the crack path pattern. Finally, the efficiency and accuracy of proposed computational algorithm is demonstrated by several numerical examples.     

Effect of hydrostatic pressure on the viscosity of failure of polymeric materials

Conclusions A setup and method were developed for studying the effect of hydrostatic pressure on the characteristics of the crack resistance of polymeric materials. The viscosity of failure of material K-4I based on butyl rubber was determined in a wide range of rates of crack propagation and hydrostatic pressures. It was found that an increase in the hydrostatic pressure increases the resistance to crack propagation in a polymeric material. The pressure-time analogy method, where the dependences of the viscosity of failure on the rate of crack growth are parallelly shifted to the value of the pressure-time shift and a generalized curve is formed, can be used for taking the effect of the pressure into consideration.Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 973–977, November–December, 1986.     

Prediction of the growth of fatigue cracks taking environmental factors into account

A model of corrosion fatigue is proposed which takes into account the main phenomena of a mechanical nature, namely, the transfer of the active agent from the month of the crack to its tip, the accumulation of mechanical damage due to cyclic loads and the breakdown of the stability conditions in the body-with-cracks — load — environment system as the reason for the propagation of the crack tip. Particular attention is devoted to the mechanism by which active agent is transferred. In addition to diffusion, convective transfer as a consequence of the change in the shape and dimensions of the crack cavity is taken into account. The results of modelling are supplemented with diagrams, which relate the rate of growth of the crack with the range of the stress intensity factor, the concentration of the agent at the mouth of the crack and the characteristics of the cycle, equal to the ratio of the extremal values of the applied stresses in each cycle. The results are compared with experimental data.     

Solution of dynamic problems in crack theory for large times

A technique is proposed for the solution of three-dimensional dynamic problems in the mathematical theory of cracks, at times larger than a characteristic value, which depends on the geometric parameters of the crack, and on the propagation velocities of longitudinal and transverse waves in the body. The stress-intensity factors are determined as functions of time, for specific types of external loading on an infinite body with a disc-shaped crack.Translated from Matematicheskie Metody i Fiziko-mekhanicheskie Polya, No. 26, pp. 24–29, 1987.     

On the computation of material forces in continuum‐atomistic modelling

Material forces govern the behavior and evolution of defects in solids. In elastic materials these forces which are associated with the Eshelby stress tensor are used to describe fracture sensitivities and can be employed to compute the J‐integral [2]. Since crack propagation begins with a variety of fundamental processes which occur within highly localized ultra–fine volume of material that constitute the fracture process zone surrounding a crack tip [3], the question of appropriate growth criteria, i.e. how far and in which direction a crack will glide under a certain loading condition is implied by the material force. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Transient response of two collinear dielectric cracks in a piezoelectric solid under inplane impacts

The paper is focused on the dynamic analysis of two collinear dielectric cracks in a piezoelectric material under the action of in-plane electromechanical impacts. Considering the dielectric permeability of crack interior, the electric displacements at the crack surfaces are governed by the jumps of electric potential and crack opening displacement across the cracks. The permeable and impermeable crack models are the limiting cases of the general one. The Laplace and Fourier transform techniques are further utilized to solve the mixed initial-boundary-value problem, and then to obtain the singular integral equations with Cauchy kernel, which are solved numerically. Dynamic intensity factors of stress, electric displacement and crack opening displacement are determined in time domain by means of a numerical inversion of the Laplace transform. Numerical results for PZT-5H are calculated to show the effects of the dielectric permeability inside the cracks, applied electric loadings and the geometry of the cracks on the fracture parameters in graphics. The observations reveal that based on the COD intensity factor, a positive electric field enhances the dynamic dielectric crack growth and a negative one impedes the dynamic dielectric crack growth in a piezoelectric solid.