Dynamic effects during instrumented impact testing

This paper presents a method to analyse dynamic effects in instrumented impact testing for fracture toughness determination. The notched specimen is replaced by a chain of nine lumped masses and the tup is connected to the impact point through a contact stiffness. A modal analysis of the mechanical system, i.e. specimen-loading machine, is achieved. In this study, it is attempted to understand the influence of the dynamic effects on the measured fracture load. Formally, two types of correction were pointed out through the presented model: calculation of effective fracture load and calculation of nominal stress or fracture toughness. The first correction is the most important.     

On the effects of higher vibration modes in the analysis of three point bend testing

Influence of higher modes of vibration in the dynamic analysis of impact three point bend specimen based on Euler-Bernoulli and Timoshenko beam theories are investigated in an attempt to predict the oscillatory behavior seen in the measured dynamic SIF history. Forced vibration of the cracked beam is analyzed by normal mode summation method. Contact force history computed using fundamental mode approximation is applied as input forcing function and the computed SIF histories are compared with finite element model and experimental data. Analytical and finite element results show that modes higher than the third have practically no influence on the notched beam response.     

A comparative study of dynamic, ductile fracture initiation in two specimen configurations

In this work a single edge notched plate (SEN(T)) subjected to a tensile stress pulse is analysed, using a 2D plane strain dynamic finite element procedure. The interaction of the notch with a pre-nucleated hole ahead of it is examined. The background material is modelled by the Gurson constitutive law and ductile failure by microvoid coalescence in the ligament connecting the notch and the hole is simulated. Both rate independent and rate dependent material behaviour is considered. The notch tip region is subjected to a range of loading rates J by varying the peak value and the rise time of the applied stress pulse. The results obtained from these simulations are compared with a three point bend (TPB) specimen subjected to impact loading analysed in an earlier work [3]. The variation of J at fracture initiation, J _c, with average loading rate J is obtained from the finite element simulations. It is found that the functional relationship between J _c and J is fairly independent of the specimen geometry and is only dependent on material behaviour.     

Effect of loading condition,specimen geometry,size-effect and softening function on double-<Emphasis Type="BoldItalic">K</Emphasis> fracture parameters of concrete

This paper presents numerical investigation of the influence of the specimen geometry, loading condition, size-effect and softening function of concrete on double-K fracture parameters. The input data needed for computation of the double-K fracture parameters are obtained from the well-known version of Fictitious Crack Model (FCM). FCM is developed for three standard specimens: three-point bend test, compact tension specimen and four-point bend test of size range 100–600 mm at relative size of initial crack length 0.3. The analysis of numerical results shows some interesting behaviour of double-K fracture parameters.     

Dynamic fracture toughness measurements in composites by instrumented Charpy testing: influence of aging

The dynamic behavior of three different fiber fabric composite laminates was studied by testing notched specimens in an instrumented Charpy machine. The registered impact force and displacement at the specimen hammer contact point were used to evaluate Mode-I fracture energy and dynamic fracture toughness. The changes in fracture toughness due to impact velocity, crack size and stacking sequence of the specimen were investigated with different degrees of aging conditions. Aging was found to significantly affect the dynamic fracture toughness, but had less effect on the static fracture toughness.     

Assessment of Analytical Models of Pure Bending of Sheet Materials Using the Digital Image Correlation Method

Bending of sheet materials is a common forming mode for shaping sheet components. Although many numerical models of bending, both analytical and numerical simulations based, are available in the literature, extensive experimental validations have been rather limited. A new bend test method and complementary three‐dimensional finite element (FE) simulation of the experiments are employed to assess the predictions from an advanced analytical and FE model of pure bending of aluminium sheet materials. The experimental set‐up developed and utilised is an open concept design that allows access to the tensile surface and through‐thickness region in the vicinity of the specimen bend line to continuously record images of the deforming specimen with two cameras. The specimen images are analysed for strains using an online strain mapping system based on digital image correction method. Tangential strain distribution results from the models in terms of material thinning in the bend region are compared with those from the experiments on AA2024 aluminium sheet material by considering the responses from the specimen edges and mid‐width regions at the bend line. Furthermore, the tangential and radial stress distributions on the through‐thickness section of the specimen from the analytical model are compared with those from the FE model. The results from experiments, FE model and analytical model are compared and discussed in the light of the experimental data and the assumptions involved in the development of the models.     

Size effect on the contact state between fracture specimen and supports in Hopkinson bar loaded fracture test

To thoroughly understand the dynamic behavior of a fracture specimen under stress wave loading, dynamic fracture test with various three-point bend (3PB) specimens are performed on the Hopkinson bar loaded experimental apparatus. The contact state between the fracture specimen and supports during the loading process is examined via stress wave propagation analysis. The experimental results show that the fracture specimen with usual dimensions does not keep contact with supports in the initial loading stage, i.e. a loss of contact phenomenon occurred. The specimen dimensions and the span of the loading apparatus are important factors affecting specimen’s contact state. The loss of contact is more obvious with increasing span under the same specimen dimensions. Conversely, the loss of contact gradually disappears with increasing specimen length or increasing width under a fixed span. Based on experimental investigations, a criterion is established to ensure the fracture specimen keep in contact with supports during dynamic fracture test.     

Influence of contact compliance on dynamic stress intensity factor variation during an impact test

Influence of the contact compliance on magnitude of oscillations of dynamic stress intensity factor (DSIF) during an impact test has been investigated numerically. It has been shown that although this magnitude is mainly determined by geometry of the specimen (namely, by combination of its relative length and relative crack depth), changes in contact stiffness affect the magnitude as well. For the range of specimen configurations and contact stiffnesses considered, the smallest DSIF oscillations were obtained for the impact specimen with relative length 5.5 and relative crack length 0.3.     

Analysis of modified split Hopkinson pressure bar dynamic fracture test using an inertia model

A split Hopkinson pressure bar (two-bar set-up) has been modified to perform dynamic three-point bend tests to measure dynamic fracture toughness, and to understand the influences of various experimental parameters, as well as inertial effects, on the dynamic material response. Modeling and analysis of the dynamic three-point bend test, as loaded by a modified split Hopkinson pressure bar, is conducted. The effects of support motion, crack propagation and plastic contact stiffness on total sample deflection are investigated. The effects of crack propagation and plastic contact stiffness on the contribution of support motion to the total sample deflection are also investigated theoretically and experimentally in this paper. Further, the effects of crack propagation and plastic contact stiffness on impactor and sample load are also addressed.     

Analysis of the dynamic responses for a pre-cracked three-point bend specimen

In this paper, shear deformation and rotary inertia was introduced into the calculation of the dynamic stress intensity factor by means of solving the stiffness of a pre-cracked three-point bend specimen. A simple formula of dynamic stress intensity factor for a pre-cracked three-point bend specimen is derived using the vibration analysis method. Dynamic three-point bending tests were performed on a uniquely modified Hopkinson pressure bar, allowing the dynamic responses of the pre-cracked specimen, such as: the natural frequency, the period of apparent specimen oscillations, the dynamic loads, and the dynamic stress intensity factor to be analyzed experimentally and theoretically.     

MODAL APPROACH FOR PROCESSING ONE- AND THREE-POINT BEND TEST DATA FOR DSIF–TIME DIAGRAM DETERMINATION. PART II—CALCULATIONS AND RESULTS

In Part I of this paper, using the modal superposition method, equations for dynamic SIF calculations are derived for an arbitrary linear model of an impact bend specimen. In this paper (Part II), modal parameters and other data which are necessary for the DSIF determination have been calculated for three types of specimen model: the Euler–Bernoulli beam model, and two- (2D) and three-dimensional (3D) solid models. For the latter two cases, calculations were performed using the finite element program ADINA. Results for the 2D model of the specimen were fitted by polynomials for a wide range of specimen geometry parameters and Poisson's ratio values. Considerable differences were observed between the beam model parameters and the 2D or 3D ones. The differences in results for the 2D and 3D models are small and mainly connected with non-uniformity of the SIF distribution along the front of a through-crack in the 3D solid. Results of processing one- and three-point bend test data reported in the literature are presented. Numerical DSIF values are compared with the experimental ones.     

弹性模量在用柔度法测量疲劳裂纹长度中的影响

用不同整体刀口设计的三点弯曲SE(B)试样做了两组疲劳裂纹扩展速率 (FCGR)试验 ,分析了弹性模量在柔度法测量疲劳裂纹长度中的影响。结果表明 ,用柔度法测量的弹性模量值偏大或偏小 ,都将影响到lg(da dN) lgΔK曲线的准确性 ,为在FCGR试验中采用SE(B)试样时整体刀口设计类型的选择提供了试验依据。     

A computational approach to the investigation of impact damage evolution in discontinuously reinforced fiber composites

 A micromechanical damage constitutive model for discontinuous fiber-reinforced composites is developed to perform impact simulation. Progressive interfacial fiber debonding and a crack-weakened model are considered in accordance with a statistical function to describe the varying probability of damage. Emanating from a constitutive damage model for aligned fiber-reinforced composites, a micromechanical damage constitutive model for randomly oriented, discontinuous fiber-reinforced composites is developed. The constitutive damage model is then implemented into a finite element program DYNA3D to simulate the dynamic behavior and the progressive damage of composites. Finally, numerical simulations for a biaxial loading test and a four-point bend impact test of composite specimens are performed to validate the computational model and investigate impact damage evolution in discontinuous fiber-reinforced composite structures. Furthermore, in order to address the influence of Weibull parameter S _o on the damage evolution in composites, parametric analysis is carried out. Received 29 April 2000     

Evaluation of Stiffness Terms for <Emphasis Type="Italic">Z</Emphasis>-cored Sandwich Panels

This paper presents a model for the stiffness terms of composite sandwich panels with structured cores (referred to as ‘z-core’ panels). Truss-cores, corrugated-cores and double-corrugated cores containing a polymeric foam were considered. The model was validated, both through finite element simulation and through comparison with the results of experimental three point bend tests on panels. A parametric study was performed to assess the performance of the different reinforced panel configurations.     

MODAL APPROACH FOR PROCESSING ONE- AND THREE-POINT BEND TEST DATA FOR DSIF-TIME DIAGRAM DETERMINATION PART I—THEORY

A hybrid experimental/numerical method for the determination of the variation in the dynamic stress intensity factor (DSIF) with time during one- or three-point bend impact tests is presented. According to the concept of hybrid methods, a DSIF–time diagram is calculated for a particular mathematical model for the specimen using experimentally registered loading as the model excitation. The simple expression for the impact DSIF–response function is derived for an arbitrary linear model of the specimen, using the modal superposition method. Finally, formulae for DSIF calculations for different types of loading approximation are derived.     

Dynamic analysis of instrumented CHARPY impact tests using specimen deflection measurement and mass-spring models

A new experimental procedure is proposed which allows the determination of parameters of mass-spring models used to analyse the CHARPY impact test. It is based on the measurement of the tup load and the specimen deflection during the impact test. The contact stiffness between the tup and the specimen is derived from the ratio of the specimen deflection over the tup displacement. The model predictions are compared with experimental results obtained from impact tests performed on PMMA specimens. This revised version was published online in August 2006 with corrections to the Cover Date.     

带惯性力修正的循环力校准方法研究

疲劳试验设备对试样施加的力值,在静态和动态时的准确度不一致。本文通过建立疲劳试验设备的物理振动模型,得出循环力的误差主要是由传感器与试样间的参振质量的惯性力引入的;推导出了惯性力对循环力幅值的影响量模型,经过对惯性力影响量的修正,最终实现了疲劳试验设备的显示力值与试样的实际受力值一致的目的。采用加速度法、刚度/位移法修正方式,建立带惯性力修正的循环力校准系统,通过比对试验和数据分析,得到了两种修正方法(加速度法、刚度/位移法)以及两种校准方法(传感器法、校准棒法)之间的结果差异小于1%,验证了惯性力修正模型的有效性。     

高速列车荷载作用下无砟轨道地基竖向耦合动力响应研究

建立高速列车荷载作用下车辆系统-无砟轨道-地基耦合动力模型,通过Fourier变换求解弹性半空间地基土体的动力控制方程,同时根据轨道底座与半空间的接触条件得到了弹性半空间表面竖向位移在频域内的表达式,再采用快速Fourier 变换求得了时域内的土体位移解。结合算例,分析了列车速度、轨道结构参数等因素对地基动力响应的影响。研究结果表明:板下调整层弹簧刚度系数越大,地基土动力响应越大,地表振动越大;底座弯曲刚度越大,地基土动力响应越小;随着列车速度增加,地基土动力响应增大;距离轨道中心处越远,地基土动力响应越小。     

A coupled FE–EFG approach for modelling crack growth in ductile materials

In this work, a coupled finite element–element free Galerkin approach has been used to model crack growth in ductile materials under monotonic and cyclic loads. In this approach, a small discontinuous domain near crack is modelled by EFG method, whereas the rest of the domain is modelled by FEM to exploit the advantages of both the methods. A ramp function has been used in the transition region to maintain the continuity between FE and EFG domains. Two plasticity models (GTN and von‐Mises) and three hardening rules (isotropic, kinematic and mixed) have been used to model the nonlinear material behaviour. Four different problems, i.e. single edge notched tension specimen, double edge notched tension specimen, compact tension specimen and three‐point bend specimen, are solved under plane strain condition using J–R curve approach. Finally, a CT specimen problem is also solved by coupled approach using three hardening rules and two plasticity models under cyclic loading.     

High yield four-point bend thin film adhesion testing techniques

Novel four-point bend specimen geometries are proposed for improved test yield over standard four-point bend specimens when measuring high-strength and ultra-thin film structures. The fracture energies of both a Cu/SiN dielectric diffusion barrier interface and a high-k/metal gate (HfO₂/Pt–Ti metal bilayer) interface are reported. Four novel specimen types were evaluated and result in significantly increased test yield as compared to the standard four-point bend specimens. The modified four-point bend specimens were fabricated by altering the crystallographic orientation, width, and thickness of the beams which make up the specimen. The mechanics of the four-point bend test are discussed for each different specimen type. The increased test yield is explained in terms of the stresses which develop in the specimen during testing, the phase angle of loading experienced for each specimen type, and the anisotropic fracture properties of single crystal silicon.