基于连续介质损伤力学的复合材料层合板低速冲击损伤模型

基于连续介质损伤力学（CDM）方法,建立了分析复合材料层合板低速冲击问题的三维数值模型。该模型考虑了层内损伤（纤维和基体损伤）、层间分层损伤和剪切非线性行为,采用最大应变失效准则预测纤维损伤的萌生,双线性损伤本构模型表征纤维损伤演化,基于物理失效机制的三维Puck准则判断基体损伤的起始,根据断裂面内等效应变建立混合模式下基体损伤扩展准则。横向基体拉伸强度和面内剪切强度采用基于断裂力学假设的就地强度（in-situ strength）。纤维和基体损伤本构关系中引入单元特征长度,有效降低模型对网格密度的依赖性。层间分层损伤情况由内聚力单元（cohesive element）预测,以二次应力准则为分层损伤的起始准则,B-K准则表征分层损伤演化。分别通过数值分析方法和试验研究方法对复合材料典型铺层层合板四级能量低速冲击下的冲击损伤和冲击响应规律进行分析,数值计算和试验测量的接触力-时间曲线、分层损伤的形状和面积较好吻合,表明该模型能够准确地预测层合板低速冲击损伤和冲击响应。     

Prediction of impact induced penetration and delamination in thick composite laminates

A static punch curve was used as the ‘structural constitutive model’ to capture the highly nonlinear behavior of the laminate in the penetration process of thick laminates. A penetration model based on a ring element was first used to simulate the static punch curve. The model was then used to predict the dynamic penetration process of large panels using the information obtained from the static punch curve of a smaller specimen. The model was shown to predict the penetration process for short and long projectiles. The area of the target that becomes delaminated during impact was shown to increase when the impact velocity was increased until the ballistic limit, beyond which the delamination area decreases with an increase in impact velocity. This phenomenon and the area that is delaminated for different size targets at different impact velocities were accurately predicted by the ring element model in conjunction with a critical shear strain criterion.     

On the influence of constitutive relation in projectile impact of steel plates

In this paper the influence of constitutive relation has been studied in numerical simulations of the perforation of 12-mm thick Weldox 460 E steel plates impacted by blunt-nosed projectiles in the sub-ordinance velocity regime. A modified version of the well-known and much used constitutive relation proposed by Johnson-Cook and both the bcc- and hcp-version of the Zerilli-Armstrong constitutive relation were combined with the Johnson-Cook fracture criterion. These models were implemented as user-defined material models in the non-linear finite element code LS-DYNA. Identification procedures have been proposed, and the different models were calibrated and validated for the target material using available experimental data obtained from tensile tests where the effects of strain rate, temperature and stress triaxiality were taken into account. Perforation tests carried out in a compressed gas gun on 12-mm-thick circular Weldox 460 E steel plates were then used as base in a validation study of plate perforation using LS-DYNA and the proposed constitutive relations. The numerical study indicated that the physical mechanisms during perforation can be qualitatively well predicted by all constitutive relations, but quantitatively more severe differences appear. The reasons for this are discussed in some detail. It was concluded that for practical applications, the Johnson-Cook constitutive relation and fracture criterion seems to be a good choice for this particular problem and excellent agreement with the experimental results of projectile impact on steel plates were obtained under the conditions investigated.     

Thermodynamically consistent coupled viscoplastic damage model for perforation and penetration in metal matrix composite materials

Accurate modeling and efficient analysis of the metal matrix composite materials failure mechanism during high velocity impact conditions is still the ultimate goal for many researchers. The objective is to develop a micromechanical constitutive model that can effectively simulate the high impact damage problem of the metal matrix composite materials. Therefore in this paper, a multiscale micromechanical constitutive model that couples the anisotropic damage mechanism with the viscoplastic deformation is presented here as a solution to this situation. This coupled viscoplastic damage model is formulated based on thermodynamic laws. Nonlinear continuum mechanics is used for this heterogeneous media that assesses a strong coupling between viscoplasticity and anisotropic damage. It includes the strong directional effect of the fiber on the evolution of the back stress and the development of the viscoplastic strain in the material behavior for high velocity impact damage related problems.     

纤维增强复合材料层板高速冲击损伤数值模拟

推导了复合材料应变率相关三维本构关系, 并将其用于复合材料层板高速冲击损伤的数值模拟。该模型在复合材料层间引入界面单元模拟层间分层, 结合三维Hashin失效准则进行单层板面内损伤识别, 引入材料刚度退化, 采用非线性有限元方法, 研究了复合材料层板高速冲击的破坏过程及层板的损伤特性。数值分析结果表明, 剩余速度预报结果与实验结果吻合较好, 层板的主要损伤形式是层间分层、 基体微裂纹和纤维断裂, 减小弹体直径、 增大铺层角度和层板厚度能够有效降低层板损伤面积。      

纤维增强复合材料层板高速倾斜冲击损伤数值模拟

根据复合材料三维黏弹性本构关系, 建立了纤维增强复合材料层板高速倾斜冲击损伤的数值分析模型。该模型在复合材料层间引入界面单元模拟层间分层, 结合三维Hashin失效准则进行单层板面内损伤识别, 引入材料刚度折减方案, 采用非线性有限元方法, 研究高速倾斜冲击下复合材料层板的破坏过程和损伤特性。研究结果表明: 层板的主要损伤形式是层间分层、 基体微裂纹和纤维断裂; 冲击速度不变而入射角度增大时, 剩余速度减小, 层板损伤面积在一定入射角度范围内有明显变化; 入射角度不变而冲击速度增大时, 剩余速度增大, 层板损伤面积在一定速度范围内也有明显变化。     

Instrumented anvil-on-rod impact experiments for validating constitutive strength model for simulating transient dynamic deformation response of metals

Instrumented anvil-on-rod impact experiments were performed to access the applicability of this approach for validating a constitutive strength model for dynamic, transient-state deformation and elastic–plastic wave interactions in vanadium, 21-6-9 stainless steel, titanium, and Ti–6Al–4V. In addition to soft-catching the impacted rod-shaped samples, their transient deformation states were captured by high-speed imaging, and velocity interferometry was used to record the sample back (free) surface velocity and monitor elastic–plastic wave interactions. Simulations utilizing AUTODYN-2D hydrocode with Steinberg–Guinan constitutive equation were used to generate simulated free surface velocity traces and final/transient deformation profiles for comparisons with experiments. The simulations were observed to under-predict the radial strain for bcc vanadium and fcc steel, but over-predict the radial strain for hcp titanium and Ti–6Al–4V. The correlations illustrate the applicability of the instrumented anvil-on-rod impact test as a method for providing robust model validation based on the entire deformation event, and not just the final deformed state.     

Numerical study of spalling in an aluminum alloy 7020-T6

Planar impact experiment is frequently used to investigate dynamic fracture of materials, particularly the spall phenomenon. Spalling is caused by the superposition of rarefaction waves reflected from free surfaces and the spall zone is found in the interior of the target. Behavior of materials in this kind of experiment is strongly affected by the stress level, time of loading and temperature. The rate and temperature effects are closely related to the thermally activated micromechanical processes [1]. Thus, in a stressed body the creation of new fracture surfaces frequently occurs with the assistance of thermal activation. For a more detailed study, it is therefore necessary to take into account the physical aspects of spalling, including dynamic plasticity and temperature coupling. This paper reports the numerical analysis performed using a finite element FE code by implementation of a cumulative fracture criterion proposed in [2] where the apparent energy of activation for spalling depends on stress, temperature and load history. Initially, a series of calculations have been run for the purely elastic case to analyze the minimum critical impact velocity needed to obtain the spall stress and it has been determined to be a function of the critical time of loading. Such analysis is of great value in designing experiments that are relatively expensive. Next, a viscoplastic constitutive relation together with the cumulative criterion, and the equation of heat conduction have been implemented in a FE code. The set of relations takes into account strain hardening, strain rate sensitivity and temperature. This series of FE calculations have been performed in order to take into account, changes of temperature due to volume dilatation as well as conversion of plastic work into heat. In addition to spalling, the free surface velocity–time profiles have been calculated for a number of impact velocities. Specific variations of the free surface velocity indicates the creation of a new fracture surface inside the target plate. The two sets of FE calculations reported in this paper led to some discussion on the influence of physical parameters on spall mechanics.     

含单边缺口混凝土梁冲击破坏的近场动力学模拟

改进了近场动力学（peridynamics,PD）微观弹脆性（prototype microelastic brittle,PMB）模型中微观模量的计算方法,解决了PMB模型的“边界效应”问题。利用改进的PMB模型计算了冲击荷载作用下单边缺口混凝土梁的破坏全过程,得到了混合型裂纹扩展的角度、路径以及裂尖最大速度,并与试验和其他数值方法模拟结果进行了对比分析,验证了改进的PMB模型的有效性。研究结果表明,近场动力学方法在模拟破坏问题时不存在网格依赖性,其本构模型自然包含了损伤与断裂的描述,是求解结构冲击破坏问题的一种有效方法。     

Analysis of the stress intensity factor dependence with the crack velocity using a lattice model

In this work, the influence of crack propagation velocity in the stress intensity factor has been studied. The analysis is performed with a lattice method and a linear elastic constitutive model. Numerous researchers determined the relationship between the dynamic stress intensity factor and crack propagation velocity with experimental and analytical results. They showed that toughness increases asymptotically when the crack tip velocity is near to a critical. However, these methods are very complex and computationally expensive; furthermore, the model requires the use of several parameters that are not easily obtained. Moreover, its practical implementation is not always feasible. Hence, it is usually omitted. This paper aims to capture the physics of this complex problem with a simple fracture criterion. The selected criterion is based on the maximum principal strain implemented in a lattice model. The method used to calculate the stress intensity factor is validated with other numerical methods. The selected example is a finite 2D notched under mode I fracture and different loads rates. Results show that the proposed model captures the asymptotic behaviour of the SIF in function of crack speed, as reported in the aforementioned models.     

Dynamic Properties of Cortical Bone Tissue: Izod Tests and Numerical Study

Bone is the principal structural component of a skeleton: it assists the load-bearing framework of a living body. Structural integrity of this component is important; understanding of its mechanical behaviour up to failure is necessary for prevention and diagnostic of trauma. In dynamic events such as traumatic falls, involvement in car crash and sports injuries, bone can be exposed to loads exceeding its structural strength and/or fracture toughness. By developing adequate numerical models to predict and describe its deformation and fracture behaviour up to fracture, a detailed study of reasons for, and ways to prevent or treatment methods of, bone fracture could be implemented. This study deals with both experimental analysis and numerical simulations of a cortical bone tissue and its response to dynamic loading. Two areas are covered: impact Izod tests for quantifying a bone's behaviour under impact loading, and a 2-D finite-element model simulating these tests. In the first part the effect of three different parameters - a cortex position, a notch depth and an energy level - on the bones tissue's response to dynamic loading was investigated. Specimens cut from anterior, posterior, medial and lateral cortex position were tested at two different levels of energy for two notch depths. In the second part, a 2D numerical model for the impact Izod test was developed using the Abaqus/Explicit finite-element software. A fully transient formulation employs an initial angular velocity of the hammer together with the real dimensions and material properties of the specimen and the impacting hammer. Three different constitutive material models - linear-elastic, elastic-plastic and viscoelastic - were implemented to compare respective results for impact parameters and fracture force. The obtained experimental results emphasize that bovine femur cortical bone has a nearly uniform fracture energy character with regard to cortex position. The simulation results showed a good agreement of the viscoelastic model with the experimental data.     

Dynamic crack propagation in large steel specimens

Dynamic fracture experiments on crack initiation and crack growth in single edge bend specimens are performed. The impact velocity is in the range of 14 to 50 m/s and the specimen size is 320×75 mm with a thickness varying from 18 to 40 mm. The experiments are recorded by high speed photography.Two different steel qualities are investigated and their constitutive characterisation are obtained from uni-axial tension tests and shear tests with strain rates in the range 10⁻⁴ to 10³ s⁻¹ and tension tests at temperatures between −196 and 600°C.One of the materials exhibits a transition from a ductile dimple fracture to a brittle cleavage fracture as the loading velocity increases and as the specimen thickness increases. Scanning electron microscope fractographs show that the density of plastic bridges within cleavage ligaments decreases with increasing impact velocity and with increasing specimen thickness. It is also noted that the local crack propagation direction deflects from the global one in cleavage fracture areas with a high density of plastic bridges.The other material fails in a ductile mode in all the investigated cases.     

Modelling deformation and damage characteristics of woven fabric under small projectile impact

Fabrics comprising highly oriented polymers possess high impact resistance and are often used in flexible armour applications. As these materials are viscoelastic, accurate modelling of their impact and perforation response requires formulation of constitutive equations representing such behaviour. This study incorporates viscoelasticity into the formulation of a model to analyse the impact of small spherical projectiles on plain-woven PPTA poly(p-phenylene-terephthalamide) fabric. The fabric is idealized as a network of viscoelastic fibre elements and a three-element viscoelastic constitutive model is used to represent polymer behaviour. Viscoelastic parameters are used to reflect intermolecular and intramolecular bond strengths as well as the static mechanical properties of fibres. Results of the theoretical analysis were compared with data from experimental tests on fabric specimens subjected to projectile impact ranging from 140 m/s to 420 m/s. Predictions of the threshold perforation velocity and energy absorbed by the fabric showed good agreement with experimental data. The proposed analysis is able to model deformation development and rupture of the fabric at the impact point. Fraying and unravelling of yarns are also accounted for. The study shows that a knowledge of static mechanical properties alone is insufficient and results in gross underestimation of impact resistance. An important parameter identified is the crimping of yarns. Yarns in woven fabric are not initially straightened out and hence part of the stretching in fabric is due to the straightening of yarns. The effect of crimping was found to be significant for high impact velocities.     

Prediction of Impact-Induced Fibre Damage in Circular Composite Plates

A simple analytical impact damage model for preliminary design analysis is developed on the basis of experimental findings observed from quasi-static lateral load and low velocity impact tests. The analytical model uses a non-linear approximation method (Rayleigh–Ritz) and the large deflection plate theory to predict the number of failed plies and damage area in a quasi-isotropic composite circular plate (axisymmetric problem) due to a point load at its centre. It is assumed that the deformation due to a static transverse load is similar to that occurred in a low velocity impact. It is found that the model, despite its simplicity, is in good agreement with finite element (FE) predictions and experimental data for the deflection of the composite plate and gives a good estimate of the number of failed plies due to fibre breakage. The predicted damage zone could be used with a fracture model developed by the second investigator to estimate the compression after impact strength of such laminates. This approach could save significant running time when compared to FE numerical solutions. Corresponding author.     

Transverse compression behavior of Kevlar KM2 single fiber

This paper investigates the quasi static transverse compression behavior of Kevlar KM2 single fiber widely used in high velocity impact (HVI) applications. The nominal stress–strain response of single fibers exhibits nonlinear inelastic behavior under transverse compression. The nonlinearity is due to both geometric and material nonlinearities. The inelastic behavior is attributed to plastic deformation and microstructural damage resulting from fibrillation and micro cracking. The experimental set up allows for the observation and measurement of compressed width in real time. An experimental methodology is presented to determine the fiber material constitutive behavior by removing the geometric nonlinearity due to the growing contact area. Results from finite element model of the test method are correlated with the experimental results to assess the accuracy of the constitutive model.     

层合复合材料冲击损伤破坏过程研究(Ⅰ)——宏观破坏准则

本文对层合复合材料在冲击载荷作用下的细观损伤和宏观损伤(分层、基体开裂、纤维断裂)的破坏机理提出了一种分析模型.该模型假设材料的非线性是由于冲击过程中的细观损伤引起的,在单元本构方程中处理;采用最大应变分量准则,处理材料的宏观损伤,并考虑了相邻层(或单元)材料状态的影响,采用节点分裂的方法模拟上述宏观损伤机理.     

混凝土圆柱体试件在低速冲击下动力效应的研究

为研究混凝土圆柱体试件在冲击荷载作用下的动力效应,利用落锤冲击试验机,对混凝土圆柱体试件在应变率100~101/s范围内进行轴向冲击试验,并采用混凝土连续面盖帽模型（CSCM）对试验过程进行数值模拟。试验中测量不同冲击速度及冲击边界下的锤头冲击力、试件轴向应变时程曲线,获取了试件破坏形态及破坏过程的高速影像,比较分析了不同冲击速度及边界条件下,试件应力、应变峰值,应变率及动力增强系数（DIF）的变化规律。结果表明：随冲击速度的增加,试件的应力、应变峰值,应变率及动力增强系数都呈增加的趋势,冲击力作用时间则减小。混凝土平均强度与冲击速度呈抛物线关系,应变率则与冲击速度呈线性关系。模拟结果表明,CSCM混凝土本构模型在低速冲击范围内,有很好的计算精度,模拟破坏形态与试验结果吻合良好。     

Transition of hertzian fracture to flexure fracture produced in glass plates by impact

The strength and fracture of a glass plate in a three-dimensional state of stress produced by the transverse impact of a spherical body is investigated. The plate is supported by a ring foundation whose radius is comparable to the thickness of the plate. A general impact theory is developed to determine the critical stresses in the plate as a function of impact velocity, plate thickness, and support span.

Impact experiments were carried out to measure the impact velocity required to fracture a glass plate specimen as a function of support span. Hertzian fracture was observed at a short span of support whereas flexure fracture was observed at a larger support span. The impact velocity of fracture was measured to be increasing with increasing support span and its corresponding critical stress of fracture was also determined.     

Multiple impact of beam-to-beam

Based on the rigid-plastic string model, the problem of a beam impacted sequentially by numerous beams with a high velocity is investigated using the wave propagation approach. Attention is focused on the response of the stricken beam. The closed-form expressions for deflection and tensile strain are obtained in the double impact case. In the multiple impact case, a general recursion formula for the tensile strain as a function of the number of the striking beam is derived. By assuming the tensile necking failure mode, the critical impact velocity to fracture the stricken beam is predicted with the impact number specified. Alternatively, with the impact velocity given, the critical impact number of the striking beam is determined. Asymptotic analyses for two limiting cases with infinite and infinitesimal time interval are performed.