Modelling brittle impact failure of disc particles using material point method

Understanding the impact failure of particles made of brittle materials such as glasses, ceramics and rocks is an important issue for many engineering applications. During the impact, a solid particle is turned into a discrete assembly of many fragments through the development of multiple cracks. The finite element method is fundamentally ill-equipped to model this transition. Recently a so-called material point method (MPM) has been used to study a wide range of problems of material and structural failures. In this paper we propose a new material point model for the brittle failure which incorporates a statistical failure criterion. The capability of the method for modelling multiple cracks is demonstrated using disc particles. Three impact failure patterns observed experimentally are captured by the model: Hertzian ring cracks, meridian cracks, and multi-fragment cracks. Detailed stress analysis is carried out to interpret the experimental observations. In particular it is shown that the experimentally observed dependence of a threshold velocity for the initiation of meridian cracks on the particle size can be explained by the proposed model. The material point based scheme requires a relatively modest programming effort and avoids node splitting which makes it very attractive over the traditional finite element method.     

Comparison study of MPM and SPH in modeling hypervelocity impact problems

Due to the high nonlinearities and extreme large deformation, the hypervelocity impact simulation is a challenging task for numerical methods. Meshfree particle methods, such as the smoothed particle hydrodynamics (SPH) and material point method (MPM), are promising for the simulation of hypervelocity impact problems. In this paper, the material point method is applied to the simulation of hypervelocity impact problems, and a three-dimensional MPM computer code, MPM3D, is developed. The Johnson–Cook material model and Mie–Grüneisen equation of state are implemented. Furthermore, the basic formulations of MPM are compared with SPH, and their performances are compared numerically by using MPM3D and LS-DYNA SPH module.     

Coupling of membrane element with material point method for fluid–membrane interaction problems

This paper proposes a coupled particle–finite element method for fluid–membrane structure interaction problems. The material point method (MPM) is employed to model the fluid flow and the membrane element is used to model the membrane structure. The interaction between the fluid and the membrane structure is handled by a contact method, which is implemented on an Eulerian background grid. Several numerical examples, including membrane sphere interaction, water sphere impact and gas expansion problems, are studied to validate the proposed method. The numerical results show that the proposed method offers advantages of both MPM and finite element method, and it can be used to simulate fluid–membrane interaction problems.     

Contact algorithms for the material point method in impact and penetration simulation

The inherent no‐slip contact constraint in the standard material point method (MPM) creates a greater penetration resistance. Therefore, the standard MPM was not able to treat the problems involving impact and penetration very well. To overcome these deficiencies, two contact methods for MPM are presented and implemented in our 3D explicit MPM code, MPM3D. In MPM, the impenetrability condition may not satisfied on the redefined regular grid at the beginning of each time step, even if it has been imposed on the deformed grid at the end of last time step. The impenetrability condition between bodies is only imposed on the deformed grid in the first contact method, while it is imposed both on the deformed grid and redefined regular grid in the second contact method. Furthermore, three methods are proposed for impact and penetration simulation to determine the surface normal vectors that satisfy the collinearity conditions at the contact surface. The contact algorithms are verified by modeling the collision of two elastic rings and sphere rolling problems, and then applied to the simulation of penetration of steel ball and perforation of thick plate with a particle failure model. In the simulation of elastic ring collision, the first contact algorithm introduces significant disturbance into the total energy, but the second contact algorithm can obtain the stable solution by using much larger time step. It seems that both contact algorithms give good results for other problems, such as the sphere rolling and the projectile penetration. Copyright © 2010 John Wiley & Sons, Ltd.     

Modelling of failure mode transition in ballistic penetration with a continuum model describing microcracking and flow of pulverized media

An Erratum has been published for this article in International Journal for Numerical Methods in Engineering 2002; 55(4):499–501. A new continuum model to describe damage, fragmentation and large deformation of pulverized brittle materials is presented. The multiple‐plane‐microcracking (MPM) model, developed by Espinosa, has been modified to track microcracking on 13 orientations under high pressure, high strain rate and high deformation. This model provides the elastic and inelastic response of the material before massive crack coalescence. When pulverization occurs, the constitutive response is modelled by means of a visco‐plastic model for granular material, which is a generalization to three dimensions of the double‐sliding theory augmented by a consolidation mechanism. The initialization of the granular model is governed by a yield surface at the onset of massive crack coalescence. This is accomplished by examining a representative volume element, modelled using the MPM model, in compression‐shear. The main advantage of this approach is to keep a continuum model at all stages of the deformation process and thus avoid the difficulties of crack representation in a discrete finite element code. This model has been implemented in LS‐DYNA and used to examine interface defeat of long rod penetrators by a confined ceramic plate. The numerical simulations are compared to experiments in order to identify failure modes. The model parameters were obtained independently by simulating plate and rod impact experiments. The proposed model captures most of the physical observations as well as failure mode transition, from interface defeat to full penetration, with increasing impact velocity. Copyright © 2002 John Wiley & Sons, Ltd.     

An asymptotic analysis of the dispersion relation of a pre-stressed incompressible elastic plate

Summary This paper concerns an asymptotic analysis of the dispersion relation for wave propagation in a pre-stressed incompressible elastic plate. Asymptotic expansions for the wave speed as a function of wavenumber and pre-stress are obtained. These expansions have important potenatial applications to many dynamic problems such as impact problems. It is shown that in the large wavenumber limit the wave speed of the fundamental modes of both symmetric and anti-symmetric motions tends to the associated Rayleigh surface wave speed, on the other hand, the wave speeds of all the harmonics tend to a single limit which is the corresponding body wave speed. It is also shown that, whereas the fundamental modes are very sensitive to changes in the underlying pre-stress, the harmonics are little affected by such changes, espcially in the small and large wavenumber limits.     

爆炸荷载作用下钢筋混凝土结构的动态响应与破坏模式的数值分析

在爆炸荷载(尤其是脉冲荷载)作用下,除了常见的弯曲破坏形态之外,钢筋混凝土结构还可能发生直剪破坏和弯剪破坏。如何准确地预测爆炸荷载作用下的钢筋混凝土结构动态响应和破坏特征是当前抗爆结构领域十分关注的课题之一。该文介绍作者近年来在这方面的一些研究成果,主要有:将三参数形式的应变速率型材料模型推广应用于二维状态下的混凝土本构关系,建立了弹粘塑性混凝土结构有限元分析方法;基于Timoshenko梁理论和弹粘塑性理论,分别采用有限差分法和有限元法,建立了土中浅埋钢筋混凝土结构动力响应和破坏模式的有限差分和有限元分析方法。对爆炸荷载作用下的典型钢筋混凝土结构计算结果表明:基于Timoshenko梁理论的有限差分分析方法和有限元分析方法能较好地模拟梁的动态响应和弯曲、弯剪以及直剪的破坏模式,而二维弹粘塑性混凝土结构有限元分析方法只能较好地模拟梁的弯曲破坏模式。     

基于显式动力学的焊点冲击失效分析

组件级高速剪切测试是用来研究芯片封装中Sn-Ag-Cu焊点冲击可靠性问题的一个重要手段。实验研究表明:随着冲击速度的增加,焊点封装结构的失效会由焊锡母材的韧性破坏向界面金属间化合物(IMC)的脆性断裂过渡;同时,其荷载-位移响应曲线形态也会发生显著的改变。为了能够更详细地了解封装结构的冲击失效行为,并进一步改进其结构设计,该文提出结合焊锡材料应变率相关的动态硬化特性,利用渐进损伤模型来模拟其动态损伤过程;同时,引进一种能够有效表征复合型裂纹扩展的内聚力模型来模拟IMC的脆性动态断裂。与实验结果的对比表明:该文提出的方法能够较为有效地表征焊点封装结构在不同冲击速度下的失效行为。     

Model-based simulation of the synergistic effects of blast and fragmentation on a concrete wall using the MPM

With the development of the material point method (MPM) that is an extension from computational fluid dynamics (CFD) to computational structural dynamics (CSD), a model-based simulation is performed in this paper to investigate the synergistic effects of blast and fragmentation on structural failure. As can be found from the open literature, the synergistic effects of blast and fragmentation have been usually simulated via a combined approach through an interface between CFD codes and CSD codes. As a consequence, numerical solutions are very sensitive to the choices of different time steps and spatial meshes for different physical phenomena, especially for the multi-physics involved in the initiation and evolution of structural failure. Hence, a coupled approach within a single computational domain seems to be necessary if objective results are needed. In this paper, a numerical procedure is proposed with the use of the MPM, so that different kinds of gradient and divergence operators could be discretized in a single computational domain without involving fixed mesh connectivity. To simulate the evolution of impact failure, the transition from continuous to discontinuous failure modes is identified via the bifurcation analysis. The potential of the proposed model-based simulation procedure is demonstrated through 1D and 2D isothermal cases including cased bomb expansion and fragmentation, blast wave expansion through a broken case, and blast and fragment impact on a concrete wall. The preliminary results obtained in this numerical study provide a better understanding of the synergistic effects on impact/blast-resistant structural design. An integrated experimental, analytical and computational effort is required to further improve the proposed procedure for general applications.     

Numerical simulation of explosive welding using the material point method

Explosive welding involves detonation of explosive, interactions of fluid-structure and plastic deformations of metal plates at the instant of the explosion. Conventional mesh-based methods such as the finite element method (FEM) and finite difference method (FDM), are limited in simulation of the explosive welding when mesh distortion and interaction of different materials occur. In order to describe process of the explosive welding and accurately predict physical parameters for the explosive welding, numerical simulation of the explosive welding which involves multi-physical phenomenon is performed by using material point method (MPM). Not only can major physical phenomena of explosion impact be well captured, but also some important technical parameters for the explosive welding can be attained based on the MPM simulation. Through the comparison with the experimental results, it is shown that the MPM is a robust tool in simulation of the explosive welding.     

Dynamically loaded light-frame wood stud walls: experimental verification of an analytical model

Light-frame wood structures may deform well beyond the elastic limit when loaded by dynamic forces such as earthquakes and sea wave impacts. This paper reports the results of an investigation into the response effects of structural modeling assumptions typically made in the design of light-frame wood structures. Two dimensional and three dimensional models based on previous research were developed to simulate such responses and examine the validity of such models. The models utilize the finite-element method and include options of nonlinear connection properties, elastic constitutive laws of wood material, large deformations, contact forces, and inertial forces. The models were subjected to an estimate of the impact load imparted by a rapidly moving sea wave. To validate the models, the results of a wave-channel experiment of a full-scale wall were used wherein the wall was instrumented with reaction load cells, displacement transducers, and strain gauges on plywood sheathing and wood framing. A closed-loop hydraulic system utilizing a time varying loading function generated the wave trains. The resulting reactions, deformations, and strains were recorded as functions of time while high-speed cameras visually recorded the failure modes and wall behavior. Material tests were conducted before and after testing to record both the observed member properties and the localized section properties. Connection tests were conducted to provide the ultimate strengths for input in the finite element model. Reasonable agreement between the experimental and analytical results over the duration of the analysis depended on the model and model assumptions as well as the result of interest. The three dimensional model captured observed failure modes including rigid-body motions after connection failures and may reliably be used to analyze similar nonlinear systems loaded well beyond the elastic limit.     

Modelling fracture in laminated architectural glass subject to low velocity impact

Standard finite element wave propagation codes are useful for determining stresses caused by colliding bodies; however, their applicability to brittle materials is limited because an accurate treatment of the fracture process is difficult to model. This paper presents a method that allows traditional wave propagation codes to model low velocity, small missile impact in laminated architectural glass such as that which occurs in severe windstorms. Specifically, a method is developed to model typical fractures that occur when laminated glass is impacted by windborne debris. Computational results of concern to architectural glazing designers are presented. This revised version was published online in November 2006 with corrections to the Cover Date.     

Analysis and reduction of quadrature errors in the material point method (MPM)

The material point method (MPM) has demonstrated itself as a computationally effective particle method for solving solid mechanics problems involving large deformations and/or fragmentation of structures, which are sometimes problematic for finite element methods (FEMs). However, similar to most methods that employ mixed Lagrangian (particle) and Eulerian strategies, analysis of the method is not straightforward. The lack of an analysis framework for MPM, as is found in FEMs, makes it challenging to explain anomalies found in its employment and makes it difficult to propose methodology improvements with predictable outcomes. In this paper we present an analysis of the quadrature errors found in the computation of (material) internal force in MPM and use this analysis to direct proposed improvements. In particular, we demonstrate that lack of regularity in the grid functions used for representing the solution to the equations of motion can hamper spatial convergence of the method. We propose the use of a quadratic B‐spline basis for representing solutions on the grid, and we demonstrate computationally and explain theoretically why such a small change can have a significant impact on the reduction in the internal force quadrature error (and corresponding ‘grid crossing error’) often experienced when using MPM. Copyright © 2008 John Wiley & Sons, Ltd.     

S-wave tracing technique to investigate the damage and failure behavior of brittle materials subjected to shock loading

To reveal the intrinsic rules of dynamic damage and failure behavior for brittle materials subjected to shock loading, a so-called transversal shear wave tracing technique (SWT) is proposed and discussed in detail in the present paper based on the wave propagation theory and the combined compression–shear impact technique. The idea of the SWT method is to diagnose the material state at real time by measuring the propagation features of loading and unloading shear waves. By using SWT technique, the preliminary experimental results of fiber-reinforced cement (FCEM) with electromagnetic particle velocity gauges embedded in the sample at different locations are reported and analyzed. By tracing the shear wave propagation, it is found that the amplitude and speed of unloading shear wave (S⁻) are related to the damage degree of the material. Particularly, S⁻ vanishes when impact velocities exceed 197 m/s, which discloses clearly a transition point from damage state to failure state of FCEM. It is significant for there is no obvious cusp to indicate such transition on the Hugoniot of FCEM. Some further studies are needed for understanding and developing of SWT method.     

Modeling ductile to brittle fracture transition in steels—micromechanical and physical challenges

Both scientists and engineers are very much concerned with the study of ductile-to-brittle transition (DBT) in ferritic steels. For historical reasons the Charpy impact test remains widely used in the industry as a quality control tool to determine the DBT temperature. The transition between the two failure modes, i.e. brittle cleavage at low temperature and ductile fracture at the upper shelf occurs also at low loading rate in fracture toughness tests. Recent developments have been made in the understanding of the micromechanisms controlling either cleavage fracture in BCC metals or ductile rupture by cavity nucleation, growth and coalescence. Other developments have also been made in numerical tools such as the finite element (FE) method incorporating sophisticated constitutive equations and damage laws to simulate ductile crack growth (DCG) and cleavage fracture. Both types of development have thus largely contributed to modeling DBT occurring either in impact tests or in fracture toughness tests. This constitutes the basis of a modern methodology to investigate fracture, which is the so-called local approach to fracture. In this study the micromechanisms of brittle cleavage fracture and ductile rupture are firstly shortly reviewed. Then the transition between both modes of failure is investigated. It is shown that the DBT behavior observed in impact tests or in fracture toughness specimens can be reasonably well predicted using modern theories on brittle and ductile fracture in conjunction with FE numerical simulations. The review includes a detailed study of a number of metallurgical parameters contributing to the variation of the DBT temperature. Two main types of steels are considered : (i) quenched and tempered bainitic and martensitic steels used in the fabrication of pressurized water reactors, and (ii) modern high-toughness line-pipe steels obtained by chemical variations and optimized hot-rolling conditions. An attempt is also made to underline the research areas which remain to be explored for improving the strength-toughness compromise in the development of steels.     

Analytical approach to the strain rate effect on the dynamic tensile strength of brittle materials

An explicit mathematical expression for the dynamic load-carrying capacity of brittle materials under dynamic tensile loads is derived based on a kind of structural-temporal failure criterion [1] and the one-dimensional longitudinal plane wave propagation model. It is shown that the dependence of the dynamic load-carrying capacity on the strain rate can be determined only by the static material parameters such as tensile strength, density, incubation time, critical failure length and constitutive constants, which verifies that the well known strain rate effect on material strength can be considered as an structural rather than material behavior, as pointed out by Cotsovos and Pavlovi? [2] recently. Moreover, it is found that, under constant strain rate, the dynamic load-carrying capacity depends also on the amplitudes of imposed boundary loads, which explains, to a significant extent, the scatter that characterizes the available experimental data. Furthermore, the derived expression can also be used as a foundation of theoretical analyses on other problems involving the strain rate effect such as dynamic size effect, dynamic failure of quasi-brittle materials and composites.     

Enhancement of the material point method using B‐spline basis functions

The material point method (MPM) enhanced with B‐spline basis functions, referred to as B‐spline MPM (BSMPM), is developed and demonstrated using representative quasi‐static and dynamic example problems. Smooth B‐spline basis functions could significantly reduce the cell‐crossing error as known for the original MPM. A Gauss quadrature scheme is designed and shown to be able to diminish the quadrature error in the BSMPM analysis of large‐deformation problems for the improved accuracy and convergence, especially with the quadratic B‐splines. Moreover, the increase in the order of the B‐spline basis function is also found to be an effective way to reduce the quadrature error and to improve accuracy and convergence. For plate impact examples, it is demonstrated that the BSMPM outperforms the generalized interpolation material point (GIMP) and convected particle domain interpolation (CPDI) methods in term of the accuracy of representing stress waves. Thus, the BSMPM could become a promising alternative to the MPM, GIMP, and CPDI in solving certain types of transient problems.     

Numerical simulation of explosively driven metal by material point method

The material point method (MPM) fully takes the advantages of both Lagrangian method and Eulerian method, and can be capable of simulating high explosive explosion problems and impact problems involving large deformation and multi-material interaction of different phases. In this paper, MPM is extended to simulate the explosively driven metal problems, and two typical explosive/metal configurations, open-faced sandwich and flat sandwich, are analyzed in detail using MPM, and numerical results are compared with Gurney solution and its corrections. Based on our MPM results, a new correction to Gurney solution is proposed to account for the lateral effects for flat sandwich configuration. MPM provides a powerful tool for studying the explosively driven metal and other explosive problems.     

Geometry dependent ductile to brittle transition of 10CrMoNbV ferritic–martensitic steel Manet II in terms of critical crack sizes

Abstract

The 10CrMoNbV Manet II cast has been selected as the reference ferritic–martensitic steel in the framework of the European Fusion Technology Programme. Charpy impact tests have been carried out in the ductile to brittle transition temperature range of this steel, such that a dynamic quasi-equilibrium has been achieved in the process zones of investigated specimens before brittle failure. This type of testing enables the evaluation of dynamic Weibull moduli and, consequently, dynamic Weibull master curves. Thus, Weibull parameters have been calculated for normal size and subsize Charpy impact specimens. The evaluated, geometry dependent dynamic Weibull master curves facilitate computation of the failure probability densities of the investigated steels as functions of scaled critical crack sizes or scaled initial defect sizes.