Crack-opening displacements and normal strains in centrally notched plates

Experimentally determined crack-opening displacements of stationary and running cracks and of inclined stationary cracks in centrally notched plates are reported in this paper. The moiré-fringe technique was used for the determination of displacement fields in test specimens of magnesium, 7075-T6 and 7178-T6 aluminum alloys. Experimentally determined crack-opening displacements were compared with corresponding re ults based on theoretical models of Westergaard, Dugdale, Craggs and Craggs-Dugdale. In addition, normal-strain fields derived from the moiré-fringe data were compared with static or dynamic strain fields of these theoretical models. The results of this investigation indicate that while the Dugdale crack is a fair model of a stationary crack in ductile materials, the Craggs crack appears to be a better representation of a running crack in the ductile materials investigated.     

On the use of crack-tip-opening displacement to predict the fracture strength of notched graphite/epoxy laminates

The fracture strength and crack-opening displacement of notched graphite/epoxy laminates were measured experimentally using the center-cracked tension-specimen geometry. Four replicate tests were conducted for a variety of laminate stacking sequences, thicknesses, and notch lengths. Most laminates exhibited extensive notch-tip damage prior to fracture. Values of crack-tip-opening displacement (CTOD) at fracture were estimated from values of crack-opening displacement measured at the crack center line. CTOD was independent of specimen crack length for the [0/±45/90] _s , [0/±45/90]_15s , [0/±45] _s , [0/±45/]_15s , and [0/90]_24s laminates. In addition, notched laminate strength was accurately predicted using a Dugdale-type model along with the estimated CTOD.Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Quebec, Canada on June 10–15, 1984.     

Observation of damage growth in compressively loaded laminates

An experimental program to determine the phenomenological aspects of composite-panel failure under simultaneous compressive in-plane loading and low-velocity transverse impact [0-75 m/s (0-250 ft/s)] is described. High-speed photography coupled with the shadow-moiré technique is used to record the phenomenon of failure propagation. The information gained from these records, supplemented by plate sectioning and observation for interior damage, has provided information regarding the failure-propagation mechanism. The results show that the failure process can be divided roughly into two phases. In the first phase the plate is impacted, and the resulting response causes interlaminar separation. In the second phase the local damage spreads to the undamaged portion of the plate through a combination of laminae buckling and further delamination. H. Chai, formerly Graduate Student and subsequently Research Fellow at California Institute of Technology     

On the description of anisotropic damage in composite laminates

A general anisotropic damage theory of cracked laminates is formulated here. The deformation of composite laminates is composed of matrix elastic strains, pseudo-elastic damage strains due to cracking and permanent damage strains due to interlaminar slip. The surface of damage initiation is constructed according to the concept of linear elastic fracture mechanics for the virgin material. After the initial damage, a pesudo-elastic damage can be used to describe the damage behaviour if interlaminar slip is negligible. Damage evolution, load induced anisotropy and interlaminar intralaminar interaction for composite laminates are examined; the latter can perturb the normality structure of damage strain rate. Explicit expressions are given for pseudo-elastic (or secant) moduli of the damaging composite laminates, under a non-interacting assumption imposed on the cracks between different families.     

Fatigue and static strength of notched and unnotched aluminum-alloy and steel specimens

This paper describes a method of presentation of fatigue data on three commonly used aircraft materials, 2024-T3 and 7075-T6 aluminum alloys and normalized SAE 4130 steel, such that variations in fatigue strength with stress-concentration factor can be shown. Comparisons of the fatigue strengths of 2024-T3 and 7075-T6 aluminum are made for the most useful range of stress-concentration factors. Static-strength results of notched and unnotched specimens of the three materials are presented to show how the strength varies with some parameters of the stress concentration. Comparison of the data with one theory for the strength of cracked specimens was made.     

Designing for tolerance to impact damage at fastener holes in graphite/epoxy laminates under compression

This paper illustrates how fracture mechanics tools may be used to estimate the residual strength of impact damaged fastener holes in composite laminates. Finite element analysis is carried out in order to study the effect of the delamination damage. It is shown that as the size of the damage is increased, a stage is reached after which a significant further increase in damage does not result in a significant decrease in residual compressive strength.     

Application of microline/grid methods to temperature dependent microscopic deformation and damage in CFRP laminates

Tensile tests of CFRP symmetric cross-ply laminates are carried out in a scanning electron microscope (SEM), and microscopic interlaminar deformation and damage near the transverse crack tip are visualized by microlines or microgrids printed on the specimen edge surface. The local deformation around the transverse crack tip is observed at 20°C, 80°C, 120°C and 160°C to evaluate the effect of thermal residual stress on the microscopic deformation and damage in the interlaminar region near the transverse crack tip. Temperature dependence of the axial crack opening displacement (COD) is also measured. The displacement field of the specimen edge surface obtained from these experimental results is compared with the theoretical model proposed by Lee, Allen and Harris. The analysis is modified to consider the temperature effect, and a good agreement is obtained between the modified theoretical predictions and experimental results.     

Monitoring damage in holed CFRP laminates using embedded chirped FBG sensors

This study proposes a new approach to monitoring the damage process in holed CFRP laminates using an embedded chirped fiber Bragg grating (FBG) sensor. To this end, we experimentally and numerically investigated the damage process and the damage-induced changes in the spectrum shape. It was experimentally confirmed that multiple types of damage (e.g., splits, transverse cracks and delamination) appeared near a hole, and that the spectrum shape of the embedded chirped FBG sensor changed as the damage extended. Our proposed simulation for the reflection spectrum considering the damage agreed with the experiments. Furthermore, this study investigated the effect of each damage pattern on the changes in the spectrum shape. Finally, based on these discussions, we present simple damage identifications with the embedded chirped FBG for the holed CFRP laminates under completely unloaded conditions.     

Fatigue damage evolution in silicon films for micromechanical applications

In this paper we examine the conditions for surface topography evolution and crack growth/fracture during the cyclic actuation of polysilicon microelectromechanical systems (MEMS) structures. The surface topography evolution that occurs during cyclic fatigue is shown to be stressassisted and may be predicted by linear perturbation analyses. The conditions for crack growth (due to pre-existing or nucleated cracks) are also examined within the framework of linear elastic fracture mechanics. Within this framework, we consider pre-existing cracks in the topical SiO₂ layer that forms on the Si substrate in the absence of passivation. The thickening of the SiO₂ that is normally observed during cyclic actuation of Si MEMS structures is shown to increase the possibility of stable crack growth by stress corrosion cracking prior to the onset of unstable crack growth in the SiO₂ and Si layers. Finally, the implications of the results are discussed for the prediction of fatigue damage in silicon MEMS structures.     

Nonlinear progressive damage model for composite laminates used for low-velocity impact

In order to effectively describe the progressively intralaminar and interlam- inar damage for composite laminates, a three dimensional progressive damage model for composite laminates to be used for low-velocity impact is presented. Being applied to three-dimensional （3D） solid elements and cohesive elements, the nonlinear damage model can be used to analyze the dynamic performance of composite structure and its failure be- havior. For the intralaminar damage, as a function of the energy release rate, the damage model in an exponential function can describe progressive development of the damage. For the interlaminar damage, the damage evolution is described by the framework of the continuum mechanics through cohesive elements. Coding the user subroutine VUMAT of the finite element software ABAQUS/Explicit, the model is applied to an example, i.e., carbon fiber reinforced epoxy composite laminates under low-velocity impact. It is shown that the prediction of damage and deformation agrees well with the experimental results.     

Numerical simulation of interlaminar damage propagation in CFRP cross-ply laminates under transverse loading

This paper proposes a numerical simulation of interlaminar damage propagation in FRP laminates under transverse loading, using the finite element method. First, we conducted drop-weight impact tests on CFRP cross-ply laminates. A ply crack was generated at the center of the lowermost ply, and then a butterfly-shaped interlaminar delamination was propagated at the 90/0 ply interface. Based on these experimental observations, we present a numerical simulation of interlaminar damage propagation, using a cohesive zone model to address the energy-based criterion for damage propagation. This simulation can address the interlaminar delamination with high accuracy by locating a fine mesh near the damage process zone, while maintaining computational efficiency with the use of automatic mesh generation. The simulated results of interlaminar delamination agreed well with the experiment results. Moreover, we demonstrated that the proposed method reduces the computational cost of the simulation.     

Residual stresses and warpage in woven-glass/epoxy laminates

Residual stresses are introduced in composite laminates during curing as a result of differential thermal expansion of the various plies. Residual stresses coupled with asymmetries in the laminate produce warpage. To study these phenomena, symmetric and asymmetric glass-fabric-reinforced laminates were fabricated. The laminate material was fully characterized by determining its physical and mechanical properties at room and elevated temperatures. Thermal strains during curing and subsequent thermal cycling were measured by means of embedded strain gages. Residual stresses were then calculated using the mechanical properties determined before. Warpage for known types of asymmetry was calculated by means of lamination theory and compared with experimental measurements using a projection moire technique. The residual stresses in the studied laminates were very low, owing to the balancing effect of the woven-fabric reinforcement. A crossplied antisymmetric laminate showed saddle-shaped warpage in agreement with the analytical prediction. Unexpected warpage found in symmetric laminates may be due to imperfections in fiber orientations and/or temperature nonuniformities during laminations. Paper was presented at the 1985 SEM Fall Conference on Experimental Mechanics held in Grenelefe, FL on Nov. 17–20.     

计及界面损伤的复合材料正交(混杂)叠层板的应力集中分析

对正交(混杂)叠层复合材料最终拉伸破坏过程中的细观应力集中问题,提出了一种修正的剪滞分析模型;研究了叠层中由于90°层的基体开裂、层间界面破坏、0°层中部分纤维断裂及纤维/基体界面损伤相互作用所导致的细观应力重新分布,获得了相应的应力集中因子和界面破坏区长度与界面剪切强度的定量关系。本文结果为进一步研究正交叠层复合材料的细观破坏机理、最终拉伸强度及协同效应等提供了重要的理论依据。     

Fatigue damage modeling in solder interconnects using a cohesive zone approach

The objective of this work is to model the fatigue damage process in a solder bump subjected to cyclic loading conditions. Fatigue damage is simulated using the cohesive zone methodology. Damage is assumed to occur at interfaces modeled through cohesive zones in the material, while the bulk material is assumed to be linear elastic. The state of damage at a cohesive zone is incorporated into the cohesive zone constitutive law by a elasticity-based damage variable. The gradual degradation of the solder material and the corresponding damage accumulation throughout the cycling process is accounted for by a damage evolution law which captures the main damage characteristics. The model prediction of the solder bump life-time is shown to be in good agreement with one of the commonly used empirical life-time prediction laws.     

金属板结构疲劳损伤二倍频兰姆波检测方法研究

针对重大基础设施安全运行需要,本文进行了金属板结构疲劳损伤非线性兰姆波检测方法研究。基于兰姆波二次谐波产生条件,确定了产生二次谐波积累增长效应的两种兰姆波模态及对应的激励频率。通过有限元仿真,研究了材料性能改变对兰姆波非线性效应的影响,证明了二倍频兰姆波非线性系数对材料性能退化表征的有效性。在此基础上,开展了金属板结构疲劳损伤非线性兰姆波检测实验研究。将极性反转方法应用于疲劳试件检测实验中,有效提高了检测信号中二倍频兰姆波的幅值和信噪比。实验结果表明,两种兰姆波模态对的二次谐波非线性系数均随疲劳损伤增加呈线性增长趋势,但基频S(0,2)模态和二倍频S(0,4)模态对对疲劳损伤检测的灵敏度更高,更适合金属板结构疲劳损伤检测。     

The fracture behavior of graphite/epoxy laminates

The results of uniaxial tensile tests conducted on a variety of graphite/epoxy laminates containing narrow rectangular slits and square or circular holes with various aspect ratios are discussed. The techniques used to study stable-crack or damage-zone growth—namely, birefringence coatings, COD gages, and microscopic observations are discussed. Initial and final-fracture modes are discussed as well as the effect of notch size and shape and laminate type on the fracture process. Characteristic lengths are calculated using the point, average and inherent flaw theories and comparisons with observations are discussed. Further, the effect of flaw geometry on stress states and deformations is assessed.Y. T. Yeow is associated with Allied Chemical Corporation, Morristown, NJ 07960; was formerly Research Associate, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061Paper was presented at 1977 SESA Spring Meeting held in Dallas, TX on May 15–20.     

含孔复合材料层合板静拉伸三维逐渐损伤分析

针对面内静拉伸纤维增强复合材料含中孔层合板，发展了参数化三维逐渐损伤模型. 该模型 可以模拟含中孔层合板损伤起始、发展及最终结构破坏整个过程，并能较好地预测含中孔层 合板的破坏模式和破坏强度. 采用所发展的模型和有限元三维逐渐损伤分析技术即应力分 析、失效判定准则及损伤过程中材料性能退化等，对其他文献所提供的9种不同类型含中孔层合板进行了损伤扩展分析及强度预测，同时对层合板的损伤基本机理、类型及其相互关联作用进行了探讨，计算结果与文献实验结果非常吻合.     

Delamination-crack propagation in ballistically impacted glass/epoxy composite laminates

For ballistically impacted glass/epoxy cross-ply laminated plates with three five-layer unidirectional laminas, high-speed photos were taken from the back of plates, illuminated from the front side. The semitransparency of the plates enabled a Nova high-speed camera to record delamination-crack propagations at speeds of up to 40,000 frames/s. The delamination crack in the fiber direction of the first (second) lamina at the first (second) interface, propagated initially at 300–400 (400–500) m/s which decreased to 200–300 (270–400) m/s during the period of observation, and decelerated to a stop within 100 (300) μs. This last velocity range (270–400 m/s) agreed well with the largest-amplitude flexural-wave velocity measured by strain gages. This is a documentation that delamination is associated with the flexural wave. A velocity gage consisting of a silver conductive paint was modified to measure propagation velocities of the generator strip which was cut from the first lamina by two through-the-thickness cracks and which initiated a sequential delamination. This generator-strip-formation velocity was higher than the measured delamination-crack-propagation velocity. This fact is consistent with the assumption that the generator strip initiates delamination cracks.