Pure mode II fracture characterization of composite bonded joints

A new data reduction scheme is proposed for measuring the critical fracture energy of adhesive joints under pure mode II loading using the End Notched Flexure test. The method is based on the crack equivalent concept and does not require crack length monitoring during propagation, which is very difficult to perform accurately in these tests. The proposed methodology also accounts for the energy dissipated at the Fracture Process Zone which is not negligible when ductile adhesives are used. Experimental tests and numerical analyses using a trapezoidal cohesive mixed-mode damage model demonstrated the good performance of the new method, namely when compared to classical data reduction schemes. An inverse method was used to determine the cohesive properties, fitting the numerical and experimental load–displacement curves. Excellent agreement between the numerical and experimental R-curves was achieved demonstrating the effectiveness of the proposed method.     

Dynamic fracture of imperfectly bonded lap joints

Summary Dynamic photoelasticity in conjunction with linear elastic fracture mechanics was utilized to study the dynamic behavior of imperfectly bonded single lap joints. Transient phenomena of propagation, reflection and diffraction of explosively generated plane elastic stress field disturbances about the tips of a crack located at the interface between the two adherends are investigated in detail. Fracture mechanics aspects of dynamic initiation under stress wave loading in similar and dissimilar lap joints are discussed.

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Dynamisches Verhalten von imperfekt geklebten, einfach überlappten Klebeverbindungen

Übersicht Das dynamische Verhalten von imperfekt geklebten einfach-überlappten Klebeverbindungen wird mit Hilfe der dynamischen Spannungsoptik im Rahmen der linear-elastischen Bruchmechanik untersucht. Die zeitlich schnell veränderlichen Vorgänge bei der Ausbreitung, Reflexion, Brechung und Beugung von explosiv erzeugten ebenen elastischen Störungen des Spannungsfeldes um die Rißspitze einer an der Trennfläche zweier (verschiedener) Materialien liegenden rißähnlichen Klebeimperfektion werden im Detail behandelt. Bruchmechanische Aspekte der dynamischen Rißinitiation an Klebefehlern unter Spannungs-wellenbelastung in monolithischen und kompositen Lappverbindungen werden diskutiert.

     

A numerical study on the SEN-TPB test applied to mode I wood fracture characterization

A numerical study involving the single edge notched-three point bending test was methodically performed to evaluate its adequacy for wood fracture characterization under mode I loading. Stress analysis along the ligament length using cohesive zone modeling allowed understating the influence of the compressive stresses induced by bending on the stress profile for geometrically similar specimens with different sizes. The stress relief region induced by the presence of the crack was identified by a stress analysis procedure along the beam length. A data reduction scheme based on the beam theory and on the crack equivalent concept was then developed considering an approach using a rectangular stress relief region. The method allows estimating the Resistance-curve without monitoring the crack length during propagation. Important remarks regarding the aspects which contribute to explain the size effect phenomenon in wood are highlighted in this study. Following the presented procedure the application of the single edge notched-three point bending test for wood fracture characterization under mode I has become considerably user-friendlier.     

Isodyne stress analysis of adhesively bonded symmetric joints

The paper presents experimental data on the actual three-dimensional stress states produced by tensile axial forces in components of adhesively bonded symmetric joints. Stress components are determined in lamination planes and in planes at various distances from lamination planes using the methods of isodyne stress analysis.The presented evidence shows that all three normal stress components exist in the components of a joint, and clearly vary with all three coordinates aligned with the length, width, and thickness of the joint. The stress state is pronounceably three dimensional and as such cannot be reliably determined using the analytical and experimental procedures based on the concept of generalized plane stress state. Thus the convenient simplified analytical and experimental procedures of stress analysis should be carefully tested for their admissibility, using as a criterion, the magnitude of acceptable error. The paper illustrates capacity of the method of analytical and optical isodynes.Paper was presented at the 1989 SEM Spring Conference on Experimental Mechanics held in Cambridge, MA on May 26–June 1.     

Stress analysis of adhesively bonded sandwich pipe joints subjected to torsional loading

Composite pipes are becoming popular in the offshore oil and gas industry. These pipes are connected to one-another by various configurations of joints. The joints are usually the weakest link in the system. In this investigation we examine the response of various joint configurations subjected to torsion, one of the most common loading conditions in piping systems. Specifically, the theoretical analysis used to evaluate the stress field in the adhesive layers of tubular and socket type bonded sandwich lap joints is presented here. The two adherends of the joints may have different thickness and materials, and the adhesive layer may be flexible or brittle. The analysis is based on the general composite shell theory. The stress concentrations at and near the end of the joints as functions of various parameters, such as the overlap length, and thickness of the adhesive layer are studied. The effects of different adherend thickness ratios, adhesive thickness and overlap length are also studied. Results obtained from the proposed analytical solutions agree well with the results obtained from finite element analysis and those obtained by other workers.     

A unified approach to geometrically nonlinear analysis of tapered bonded joints and doublers

A unified approach for approximating the adhesive stresses in a bond line of a tapered bonded joint or doubler is delineated within the framework of a geometrically nonlinear analysis. The approach follows the Goland–Reissner solution method for a single-lap joint and involves a two-step analysis procedure. The approach also allows for the analysis of a tapered bonded joint and doubler with non-identical adherends. In the first step of the procedure, the two adherends are assumed to be rigidly bonded, and the nonlinear moment distribution along the joint is determined. Since the bending moment solution in this step is simple, it will be derived in closed-form using elementary functions. In the second step analysis, only the overlapped area of the joint is considered with the nonlinear bending moments obtained from the first step at the end of the overlap prescribed as one of its boundary conditions. This latter problem is then solved by using the multi-segment method of integration [Kalnins, A., 1964. Analysis of shell of revolutions subjected to symmetrical and non-symmetrical loads. Journal of Applied Mechanics 31, 1355–1365]. In contrast to the original Goland–Reissner solution method [Goland, M., Reissner, E., 1944. The stresses in cemented joints. Journal of Applied Mechanics 11, A17–A27], the second step analysis can be conducted within both geometrically linear theory and an approximate geometrically nonlinear theory.     

Numerical prediction of fracture in the Taylor test

A flat-nosed cylinder moving at a sufficiently high impact velocity in the classical Taylor test will always fracture. In this paper, fracture phenomena and fracture mechanisms in the Taylor test are investigated numerically based on a recently developed ductile fracture locus with the cut-off value for the negative stress triaxiality at −1/3. The impact velocity of the projectile ranges from 240 m/s to 600 m/s. The lower velocity is applied to a less ductile 2024-T351 aluminum alloy cylinder while the higher velocity is introduced for more ductile Weldox 460 E steel. Three distinct fracture modes are recreated numerically: the confined fracture inside the cylinder, the shear cracking on the lateral surface, and the petalling, all of which are consistent with experimental results presented in the open literature. It is found that a more ductile cylinder tends to fail by petalling while a less ductile one by shear cracking. Confined fracture is a common failure mode for both materials, which occurs in a wide range of the impact velocity. The ductile fracture criterion with the cut-off value predicts realistic fracture patterns for short cylinders deforming predominantly under compression.     

Numerical and experimental characterization of a double-orifice synthetic jet actuator

A complete investigation of a double-orifice synthetic jet actuator, focused on the device frequency response in terms of jet velocity, has been carried out. Numerical simulations have shown that, in many operation conditions, the flow within the actuator cavity can be considered as divided in two sub-volumes, each characterized by its own flow field. An analytical approach, based on the previous consideration, has allowed to obtain simple relationships for the three resonance frequencies and to provide further insights on the jets formation. The model has been validated through experimental tests carried out on two actuators manufactured in-house, having different geometrical and mechanical characteristics. Comparisons with the behavior of the twin single-orifice device have been discussed and useful considerations on the prediction of the actual formation of the synthetic jet are included .     

Effects of adhesive thickness on global and local Mode-I interfacial fracture of bonded joints

The interfacial fracture of adhesively bonded structures is a critical issue for the extensive applications to a variety of modern industries. In the recent two decades, cohesive zone models (CZMs) have been receiving intensive attentions for fracture problems of adhesively bonded joints. Numerous global tests have been conducted to measure the interfacial toughness of adhesive joints. Limited local tests have also been conducted to determine the interface traction-separation laws in adhesive joints. However, very few studies focused on the local test of effects of adhesive thickness on the interfacial traction-separation laws. Interfacial toughness and interfacial strength, as two critical parameters in an interfacial traction-separation law, have important effect on the fracture behaviors of bonded joints. In this work, the global and local tests are employed to investigate the effect of adhesive thickness on interfacial energy release rate, interfacial strength, and shapes of the interfacial traction-separation laws. Basically, the measured laws in this work reflect the equivalent and lumped interfacial fracture behaviors which include the cohesive fracture, damage and plasticity. The experimentally determined interfacial traction-separation laws may provide valuable baseline data for the parameter calibrations in numerical models. The current experimental results may also facilitate the understanding of adhesive thickness-dependent interface fracture of bonded joints.     

Stress-function variational method for interfacial stress analysis of adhesively bonded joints

High interfacial stresses at the free edges of adherends are responsible for the debonding failure of adhesively bonded joints (ABJs). In this paper, a general stress-function variational method is formulated to determinate the interfacial shear and normal (peeling) stresses in ABJs in high accuracy. By extending authors’ prior work in stress analysis of bonded joints (Wu and Jenson, 2011), all the planar stress components in the adherends and adhesive layer of an ABJ are expressed in terms of four unknown interfacial stress functions, which are introduced at the upper and lower surfaces of the adhesive layer. A set of governing ordinary differential equations (ODEs) of the four interfacial stress functions is obtained via minimizing the complimentary strain energy of the ABJ, which is further solved by using eigenfunctions. The obtained semi-analytic stress field can satisfy all the traction boundary conditions (BCs) of the ABJ, especially the stress continuity across the bonding lines and the shear-free condition at the ends of adherends and adhesive layer. As an example, the stress field in an adhesively single-sided strap joint is determined by the present method, whose numerical accuracy and reliability are validated by finite element method (FEM) and compared to existing models in the literature. Parameter studies are performed to examine the dependencies of the interfacial stresses of the exemplified ABJ upon the geometries, moduli and temperature change of the adherends and adhesive layer, respectively. The present method is applicable for scaling analysis of joint strength, optimal design of ABJs, etc.     

Dynamic fracture analysis of adhesive bonded material under normal loading

Dynamic fracture behavior of a Griffith crack along the interface of an adhesive bonded material under normal loading is studied. The singular integral equations are obtained by employing integral transformation and introducing dislocation density functions. By adopting Gauss-Jacobi integration formula, the problem is reduced to the solution of algebraic equations, and by collocation dots method. their solutions can be obtained Based on the parametric discussions presented in the paper, the following conclusions can be drawn： （1） Mode I dynamic stress intensity factor （DSIF） increases with increasing initial crack length and decreasing visco-elastic layer thickness, revealing distinct size effect; （2） The influence of the visco-elastic adhesive relaxation time on the DSIF should not be ignored.     

胶层吸湿对单搭接接头影响的数值模拟

在建立胶桔剂吸涅本构模型的基础上,用弹塑性有限元法研究了聚丙烯酸酯胶层吸涅程度对单搭接接头上胶层中应力分布的影响.结果表明:随着胶层吸湿程度增加,单搭接接头上胶瘤处的峰值应力显著降低.对水分从搭接区两侧渗入胶层的总宽度变化时胶层中的应力分布作了研究,发现随渗入总宽度的增加,胶层中的等效应力Seqv峰值下降.因水分渗入后引起胶层溶胀,在胶瘤过渡到中间胶层的拐角处会产生严重变形,可能导致该处发生脱粘.     

The dynamic behaviour of a piezoelectric actuator bonded to an anisotropic elastic medium

Surface-bonded piezoelectric actuators can be used to generate elastic waves for monitoring damages of composite materials. This paper provides an analytical and numerical study to simulate wave propagation in an anisotropic medium induced by surface-bonded piezocermic actuators under high-frequency electric loads. Based on a one-dimensional actuator model, the dynamic load transfer between a piezoceramic actuator and an anisotropic elastic medium under in-plane mechanical and electrical loading is obtained. The wave propagation induced by the surface-bonded actuator is also studied in detail by using Fourier transform technique and solving the resulting integral equations in terms of the interfacial shear stress. Typical examples are provided to show effects of the geometry, the material combination, the loading frequency and the material anisotropy of the composite upon the load transfer and the resulting wave propagation.     

Analysis of tapered ENF specimen and characterization of bonded interface fracture under Mode-II loading

An engineering approach for evaluating the shear-mode (Mode-II) fracture toughness of wood–wood and wood-composite bonded interfaces is presented. A tapered beam on elastic foundation model is developed to analyze and design a linear tapered end-notched flexure (TENF) specimen for fracture tests of bonded interfaces. The elastic foundation model is verified numerically by finite element analysis and experimentally by compliance calibration tests, which demonstrate that the present model can accurately predict the compliance and compliance rate-change of the specimen, and with proper design, an approximate constant rate of compliance change with respect to crack length can be achieved. The proposed TENF specimen can be used for Mode-II fracture toughness evaluations with reasonable confidence in the linearity of compliance crack-length relationship. The fracture of wood–wood and wood-composite bonded interfaces under Mode-II loading is experimentally evaluated using the proposed TENF specimen, and the corresponding values of critical strain energy release rate are obtained. The modeling technique and testing method presented can be efficiently used for characterization of Mode-II fracture of bonded bimaterial interfaces.     

高应变率下断裂韧性实验的数值模拟

采用有限元软件ANSYS/LS-DYNA程序对静态和冲击荷载作用下的含裂纹半圆弯曲(SCB)实验进行了数值模拟。根据静态实验的模拟结果,提出了适合复合型加载的Ⅰ型应力强度因子拟合公式,采用该公式计算应力强度因子的最大误差不超过10%。动态实验的模拟结果表明:对于纯Ⅰ型加载的SCB实验,动态应力强度因子随着试样半径、支座间距以及相对裂纹长度的变化呈现规律性变化;当试样半径小于60mm、相对支座间距为1.2、相对裂纹长度在0.1~0.4范围内时,惯性效应的影响较小,采用静态拟合公式计算裂尖的动态应力强度因子的误差约10%;对于复合型加载的SCB实验,当相对裂纹长度为0.2~0.4、裂纹倾角在10°~40°范围内时,采用静态拟合公式计算裂尖的动态应力强度因子的误差小于10%。     

An analytical investigation on thermomechanical stress analysis of adhesively bonded joints undergoing heat conduction

Thermomechanical loading, in the same way that mechanical loading can cause significant stress violations, may give rise to significant stress variations and concentrations and in some circumstances can result in structural destruction or even failure. This clearly shows the importance of accurate stress analysis of thermal-loaded structures. This paper presents three-dimensional thermomechanical stress analysis of heterogeneous adhesively bonded joints undergoing steady-state one-dimensional heat conduction using the full layerwise theory. In this approach, the fully coupled three-dimensional governing equilibrium equations are derived generally for an orthotropic joint based on the use of variational calculus and the principle of minimum total potential energy. The through-thickness temperature distribution is determined using the equivalent thermal-resistant model and is rewritten in the layerwise form. The governing equations of equilibrium then are analytically solved using the state space approach. The accurate results presented in this study are compared and verified via analytical as well as numerical investigations, and the study shows rapid converging solutions.     

冲击载荷下镁铝合金裂纹动态扩展过程的数值模拟

采用基于黏聚裂纹模型的扩展有限元方法,开展了镁铝合金结构冲击破坏过程的数值模拟研究。通过镁铝合金三点弯曲试样冲击实验,获得了不同子弹撞击速度下试样的冲击破坏模式。在此基础上,建立了实验结构的扩展有限元模型,并采用最大主应力准则,以及含损伤型的本构关系模拟材料的冲击断裂行为。对于裂纹尖端附近区域,采用黏聚裂纹模型模拟裂纹的断裂过程。对子弹速度分别为12.2、15.1、26.3 m/s的3种工况下镁铝合金试样的动态破坏过程进行了数值模拟研究,获得了与实验相一致的断裂模式。计算结果表明,试样以Ⅰ型断裂模式为主,裂纹沿初始预制裂纹方向扩展。当裂纹扩展到一定程度后,在试样韧带区域被撞击端附近,由于应力波及边界效应导致该区域处于复杂应力状态,试样出现复合型断裂模式,裂纹偏离原扩展路径,与本文实验结果相吻合。     

Numerical failure analysis of a stretch-bending test on dual-phase steel sheets using a phenomenological fracture model

Advanced High Strength Steels (AHSS) are increasingly used in automotive industry due to their superior strength and substantial weight advantage. However, their compromised ductility gives rise to numerous manufacturing issues. One of them is the so-called ‘shear fracture’ often observed on tight radii during stamping processes. Since traditional approaches, such as the Forming Limit Diagram (FLD), are unable to predict this type of fractures, great efforts have been made to develop failure criteria that could predict shear fractures. In this paper, a recently developed Modified Mohr–Coulomb (MMC) ductile fracture criterion (Bai and Wierzbicki, 2010) is adopted to analyze the failure behavior of a Dual Phase (DP) steel sheet during stretch-bending operations. The plasticity and ductile fracture of the present sheet are fully characterized by a Hill’48 orthotropic model and a MMC fracture model, respectively. Finite element models with three different element types (3D, shell and plane strain) were built for a Stretch Forming Simulator (SFS) test (Shih and Shi, 2008), numerical simulations with four different R/t values (die radius normalized by sheet thickness) were performed. It has been shown that the 3D and shell element simulations can predict failure location/mode, the upper die load–displacement responses as well as wall stress and wrap angle at the onset of fracture for all R/t values with good accuracy. Furthermore, a series of parametric studies were conducted on the 3D element model, and the effect of tension level (clamping distance), tooling friction, mesh size and fracture locus on failure modes and load–displacement responses were investigated.     

Lattice model applied to the fracture of large strain composite

An improved lattice model is developed to simulate the fracture behavior of large strain composite. Based on equivalent relation between the continuum and the lattice model for small deformation, the equivalent relation between large strain continuum and improved lattice model is established by introducing large strain elastic law into the lattice system. The theory can simulate large deformation. The program of large strain lattice model simulates several representative problem of large strain elasticity. The results agree with the theoretical results. Assumed failure criterion is used to describe the fracture process of large strain elasticity and large strain composite. The improved lattice model provides an effective method for fracture simulation of large strain composite.     

冲击荷载作用下粘土孔隙水压的数值分析

为了分析冲击荷载作用下粘土的孔隙水压力的增长规律,为分析粘土介质的动态响应、动力固结加固提供理论依据,将冲击瞬态荷载简化为三角形荷载,通过编制瞬变动态弹塑性有限元程序,对冲击荷载作用下粘土孔隙水压的动态响应进行了模拟,得出了冲击荷载作用下粘土孔隙水压的增长规律,发现孔隙水压力峰值无论是随水平距离还是随深度的增加均呈指数形式衰减,和实际工程施工中孔隙水压的监测数据相吻合。