Measurement of fatigue damage in composite materials

Numerical results for the stress state around a circular hole in a [0/±45/0]_s boron-epoxy plate under tensile loading are presented. This serves as a model for the initial stress state around the hole during fatigue loading. Comparison is drawn with experimental results for a fatigued specimen obtained from thermography and radiography. Using these results, an interpretation of the effects of the initial stress state on the thermal behavior and on failure initiation is given. This interpretation shows that the circumferential normal stresses are responsible for the initial heat generation and failure initiation in the fatigued specimen.     

Fatigue damage of APC-2 composite assessed from material degradation and non-destructive evaluation data

Quasi-isotropic 45° APC-2 specimens are fatigued under constant amplitude stress reversal load condition. Fatigue induced degradation of the mechanical properties is correlated to data obtained from non-destructive evaluation. C-scan readings were used to define a generic damage severity factor D. It refers to the current fatigue damage state and accounts for the varying severity of damage at the different specimen locations. Analytical expressions are developed to relate D to the axial stiffness, residual strength and interlaminar shear strength. An indication of damage tolerance can thus be made for evaluating the integrity of structural components.     

Structural damage localization and evaluation based on modal data via a new evolutionary algorithm

This paper is intended to present a method for the localization and evaluation of damage in plates based on the changes in natural frequencies and mode shapes of the damaged plate using an optimization approach. The colonial competitive algorithm is employed to detect damage (or damages) in plates by optimizing a damage function. The performance of the proposed method is demonstrated by implementing the technique to two examples; a shear wall and a four-fixed supported plate with and without modal data noise including one or a large number of damages. The results confirm the applicability and efficiency of the presented method in detecting damage localization and quantification in the shear walls. Furthermore, the proposed method is implemented to the four-fixed supported plate aimed at demonstrating the high sensitivity of the proposed method in quantitative estimation of damaged plate structures. Finally, the reliability of the presented method is explored through the comparison of the obtained results and those of the other methods. It is concluded that the proposed method can be viewed as a powerful and robust method for structural damage detection in plate structures.     

Thermographic stress analysis of composite materials

Several critical aspects of stress measurements in composite materials by thermographic stress analysis (TSA; also SPATE method) have been investigated. The emphasis is on the observed effects of thermal-expansion coefficients with positive and negative signs, thickness of surface coating, and absolute temperature increases in the material due to cyclic loading. Heat transfer and mean stress effects are also discussed.     

Ultrasonic-image evaluation of microstructural damage accumulation in materials

Ultrasonic imaging techniques for portraying and evaluating cumulative internal microstructural damage in engineering materials are described. A quantitative delineation of the damage is made in terms of acoustic attenuation obtained from computer analyses of digitized ultrasonic images. Acoustic attenuation data are a basic ingredient in previously developed models of damage processes in materials. The ultrasonic imaging methodology has been developed using filled polymer (inert solid rocket-propellant) samples subjected to progressive uniaxial tensile strain. Successive ultrasonic images taken at various levels of applied strain display dewetting and the evolving microvoid formation/growth which occurs. Both initially intact material and that with pre-existing cracks are of interest. Changes in acoustic attenuation with strain, derived from the processing of digital images, have provided results as to the degree of preferential damage accumulation at sites of filler particle agglomerations appearing on the ultrasonic images. Also, the quantitative extent of an asymmetry in the damage-field distribution near the tips of an extending crack was determined in precracked material. Iso-attenuation type contours generated by computer reveal that kidney-shaped damage zones occur in the neighborhood of the propagating crack tips, reminiscent of the plastic-zone shapes near crack tips in ductile metals under strain. Ultrasonic images of precracked samples show that before crack extension begins, the material damage in the neighborhood of the crack already extends over a relatively large volume of the specimen. G.C. Knollman is Senior Staff Scientist and Senior Member, Mechanics and Maternals Engineering Laboratory     

Creep damage and life analysis of anisotropic materials

Summary  This paper provides a short survey of some recent advances in the mathematical modelling of materials behaviour under creep conditions. The tertiary creep phase is accompanied by the formation of microscopic cracks on the grain boundaries in such a way so that damage accumulation occurs. The paper is divided into three parts. Firstly, the damage state in a uniaxial tension specimen is discussed and the time to rupture calculated. The second part is concerned with the creep behaviour of materials in multiaxial stress. Because of its microscopic nature, damage generally has an anisotropic character even if the material was originally isotropic. The fissure's orientation and length cause anisotropic macroscopic behaviour. Therefore, damage in an isotropic or anisotropic material, which is in a state of multiaxial stress, can only be described in a tensorial form. Thus, tensorial constitutive and evolution equations have been developed. Some examples for practical use are discussed. Finally, some own experiments are mentioned which have been carried out in order to validate the mathematical modelling. Received 16 July 1999; accepted for publication 8 March 2000     

Mesomechanics of deformation and short-term damage of linear elastic homogeneous and composite materials

The structural theory of microdamage of homogeneous and composite materials is generalized. The theory is based on the equations and methods of the mechanics of microinhomogeneous bodies with stochastic structure. A single microdamage is modeled by a quasispherical pore empty or filled with particles of a damaged material. The accumulation of microdamages under increasing loading is modeled as increasing porosity. The damage within a single microvolume is governed by the Huber-Mises or Schleicher-Nadai failure criterion. The ultimate strength is assumed to be a random function of coordinates with power-law or Weibull one-point distribution. The stress-strain state and effective elastic properties of a composite with microdamaged components are determined using the stochastic equations of elasticity. The equations of deformation and microdamage and the porosity balance equation constitute a closed-form system of equations. The solution is found iteratively using conditional moments. The effect of temperature on the coupled processes of deformation and microdamage is taken into account. Algorithms for plotting the dependences of microdamage and macrostresses on macrostrains for composites of different structure are developed. The effect of temperature and strength of damaged material on the stress-strain and microdamage curves is examined __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 6, pp. 3–42, June 2007.     

Nondestructive evaluation of damage in composite structures using modal parameters

The problem of using measured modal parameters to detect and locate damage in structures made of fiberreinforced composites is investigated. Recent work in this area using modal sensitivity equations is used in conjunction with internal-state variable constitutive theory to derive a set of damage-detection equations which are used to predict, from changes in measured modal parameters, the current value of the internal-state variables in each finite element. The value of the internal-state variable determines the extent of damage at a given location. Numerical examples involving damaged composite beams are used to demonstrate the capability of the theory to predict the exact location and the severity of damage. To provide experimental evidence to support the theory, mechanical and modal tests are performed on a [0,90₃] _s laminated composite beam in the undamaged state and in three additional states of progressive damage. At each stage of damage, edge replications are taken to determine the crack density along the length of the beam. The predicted values of the internal-state variables, obtained from the modalsensitivity equations using measured modal information, are compared with the values of the internal-state variables obtained from crack-density measurements along the length of the beam. Good agreement between the predicted and the measured values is found.     

Coupled twoscale analysis of fiber reinforced composite structures with microscopic damage evolution

The simultaneous twoscale analysis of unidirectionally fiber reinforced composite structures with attention to damage evolution is the objective of the contribution. The heterogeneous microstructure of the composite represents the microscale, whereas the laminate or the structural component are addressed as the macroscale. The macroscale is conventionally discretized by the finite element method (FEM). The generalized method of cells (GMC) in its efficient stress based formulation serves as the discrete microscale model. The stiff and brittle fibers behave linearly elastic. The epoxy resin is described by the nonlinear-elastic model of Ramberg–Osgood. By introducing microcrack models, the damage of the epoxy matrix under combined tensile and shear loading is taken into account. The cell boundaries of the micromodel are used to locate microscopic cracks deterministically. Interface models for the representation of damage in the matrix phase as well as for the weakening of the fiber–matrix-bond are used. This approach circumvents the need for the regularization, as it would be necessary for continuum damage models with softening characteristics. Hence, the micromodel is numerically stable and convergent. The GMC allows to obtain the consistently linearized constitutive tensor in the case of nonlinear material behavior in a simple and straight forward manner which is easily implemented in comparison to micromodels based on the finite element technique. The damage evolution on the microscale manifests itself macroscopically in the degradation of the homogenized stiffnesses.     

复合材料层合板冲击损伤近场动力学模型与分析

近场动力学(简称PD)理论通过域内积分建立物质基本运动方程。不同于传统理论中通过微分建立运动方程的方法,该理论对场函数没有连续性的要求,因而适合求解各类不连续问题。基于此,本文建立了正交各向异性单层板PD理论模型,进而引入单层板层间作用,发展了正交各向异性层合板PD模型及其损伤模型,并模拟了各向同性与各向异性层合板冲击损伤;通过对比分析,对模型的有效性进行了验证。     

Deformation and long-term damage of homogeneous and composite materials of stochastic structure (Review)

The studies of mathematical models for the coupled processes of deformation and long-time damage of stochastic composite materials are systematized. Damage is modeled by stochastically arranged micropores. The damage of a single microvolume is characterized by its stress-rupture strength determined by the dependence of the time to brittle fracture on the difference between the equivalent stress and its limit, which is the ultimate strength, according to the Huber–Mises or Schleicher–Nadai criteria, and assumed to be a random function of coordinates. The equation of damage balance at an arbitrary time and the equations relating macrostresses and macrostrains constitute a closed system. Algorithms of calculating the time dependence of microdamage and macrostresses are developed. The effect of temperature and nonlinearity on the curves is studied     

Spectral analysis of localization in nonlocal and over-nonlocal materials with softening plasticity or damage

The paper shows that spectral wave propagation analysis reveals in a simple and clear manner the effectiveness of various regularization techniques for softening materials, i.e., materials for which the yield limits soften as a function of the total strain. Both plasticity and damage models are considered. It is verified analytically in a simple way that the nonlocal integral-type model with degrading yield limit depending on the total strain works correctly if and only one adopts an unconventional nonlocal formulation introduced in 1994 by Vermeer and Brinkgreve (and in 1996 by Planas, and by Strömberg and Ristinmaa), which is here called, for the sake of brevity, ‘over-nonlocal’ because it uses a linear combination of local and nonlocal variables in which a negative weight imposed on the local variable is compensated by assigning to the nonlocal variable weight greater than 1 (this is equivalent to a nonlocal variable with a smooth positive weight function of total weight greater than 1, normalized by superposing a negative delta-function spike at the center). The spectral approach readily confirms that the nonlocal integral-type generalization of softening plasticity with an additive format gives correct localization properties only if an over-nonlocal formulation is adopted. By contrast, the nonlocal integral-type generalization of softening plasticity with a multiplicative format provides realistic localization behavior, just like the nonlocal integral-type damage model, and thus does not necessitate an over-nonlocal formulation. The localization behavior of explicit and implicit gradient-type models is also analyzed. A simple analysis shows that plasticity and damage models with gradient-type localization limiter, whether explicit or implicit, have very different localization behaviors.     

An experimental evaluation of the slotted-tension shear test for composite materials

The slotted-tension shear test provides an accurate method of measuring the inplane shear response of fiber-reinforced composite materials. Data from the slotted-tension test is compared with rail, ±45-deg tension, modified lap-shear and off-axis shear tests. It is shown that reinforced materials of any combination of fibers and fiber orientation can be tested using the new shear-testing technique.     

Micromechanical analysis of damage in saturated quasi brittle materials

In this paper, we propose a micromechanical analysis of damage and related inelastic deformation in saturated porous quasi brittle materials. The materials are weakened by randomly distributed microcracks and saturated by interstitial fluid with drained and undrained conditions. The emphasis is put on the closed cracks under compression-dominated stresses. The material damage is related to the frictional sliding on crack surface and described by a local scalar variable. The effective properties of the materials are determined using a linear homogenization approach, based on the extension of Eshelby’s inclusion solution to penny shaped cracks. The inelastic behavior induced by microcracks is described in the framework of the irreversible thermodynamics. As an original contribution, the potential energy of the saturated materials weakened by closed frictional microcracks is determined and formulated as a sum of an elastic part and a plastic part, the latter entirely induced by frictional sliding of microcracks. The influence of fluid pressure is accounted for in the friction criterion through the concept of local effective stress at microcracks. We show that the Biot’s effective stress controls the evolution of total strain while the local Terzaghi’s effective stress controls the evolution of plastic strain. Further, the frictional sliding between crack lips generates volumetric dilatancy and reduction in fluid pressure. Applications of the proposed model to typical brittle rocks are presented with comparisons between numerical results and experimental data in both drained and undrained triaxial tests.     

Analytical and numerical analysis of frictional damage in quasi brittle materials

Frictional sliding and crack growth are two main dissipation processes in quasi brittle materials. The frictional sliding along closed cracks is the origin of macroscopic plastic deformation while the crack growth induces a material damage. The main difficulty of modeling is to consider the inherent coupling between these two processes. Various models and associated numerical algorithms have been proposed. But there are so far no analytical solutions even for simple loading paths for the validation of such algorithms. In this paper, we first present a micro-mechanical model taking into account the damage-friction coupling for a large class of quasi brittle materials. The model is formulated by combining a linear homogenization procedure with the Mori–Tanaka scheme and the irreversible thermodynamics framework. As an original contribution, a series of analytical solutions of stress–strain relations are developed for various loading paths. Based on the micro-mechanical model, two numerical integration algorithms are exploited. The first one involves a coupled friction/damage correction scheme, which is consistent with the coupling nature of the constitutive model. The second one contains a friction/damage decoupling scheme with two consecutive steps: the friction correction followed by the damage correction. With the analytical solutions as reference results, the two algorithms are assessed through a series of numerical tests. It is found that the decoupling correction scheme is efficient to guarantee a systematic numerical convergence.     

Damage and fracture evaluation of granular composite materials by digital image correlation method

This paper presents the applications of digital image correlation technique to the mesoscopic damage and fracture study of some granular based composite materials including steelfiber reinforced concrete, sandstone and crystal-polymer composite. The deformation fields of the composite materials resulted from stress localization were obtained by the correlation computation of the surface images with loading steps and thus the related damage prediction and fracture parameters were evaluated. The correlation searching could be performed either directly based on the gray levels of the digital images or from the wavelet transform (WT) coefficients of the transform spectrum. The latter was developed by the authors and showed higher resolution and sensitivity to the singularity detection. Because the displacement components came from the rough surfaces of the composite materials without any coats of gratings or fringes of optical interferometry, both surface profiles and the deformation fields of the composites were visualized which was helpful to compare each other to analyze the damage of those heterogeneous materials. The project supported by the National Natural Science Foundation of China (10125211 and 10072002), the Scientific Committee of Yunnan Province for the Program of Steel Fiber Reinforced Concrete, and the Institute of Chemical Materials, CAEP at Mianyang     

A new hybrid technique for in-plane characterization of orthotropic materials

In this paper we present a novel hybrid procedure for the in-plane mechanical characterization of orthotropic materials. The material identification reverse engineering problem is solved by combining speckle interferometry and numerical optimization. The rationale behind the entire process is the following: for any specimen to be characterized and which has been subjected to some loading condition, it is possible to express the difference between experimental data and analytical/numerical predictions by means of an error function ψ, which depends on the elastic constants of the material. The ψ error will decrease as the elastic constants come close to their target values. Here, we build the ψ function as the difference between the displacement field measured with speckle interferometry and its counterpart computed by means of finite element analysis. Since the ψ function is highly non-linear, it has to be optimized with a global optimization algorithm, which perform a random search in the elastic constants design space. The hybrid material identification process finally allows us to determine values of the elastic constants. In order to prove the feasibility of the present approach, we have determined the in-plane elastic properties of an eight-ply composite laminate (woven fiberglass-epoxy) used as a substrate for printed circuit boards. The results indicate that the procedure proposed in this paper was able to accurately characterize the material under investigation. Remarkably, the elastic constants found by the identification procedure were less than 0.7% different from their target values, while the residual error between the displacements measured by speckle interferometry and those computed at the end of the optimization process was less than 3%. L. Lamberti is an Assistant Professor, and C. Pappalettere (SEM Member and President of the Italian Society of Stress Analysis) is Professor of Mechanical Engineering and Experimental Mechanics, Politecnico di Bari, Dipartimento di Ingegneria Meccanica e Gestionale, Viale Japigia 182, 70126 Bari, Italy     

Topological design of structures and composite materials with multiobjectives

This paper studies the influence of heat conduction in both structural and material designs in two dimensions. The former attempts to find the optimal structures with the maximum stiffness and minimum resistance to heat dissipation and the latter to tailor composite materials with effective thermal conductivity and bulk modulus attaining their upper limits like Hashin–Shtrikman and Lurie–Cherkaev bounds. In the part of structural topology optimization of this paper solid material and void are considered respectively. While in the part of material design, two-phase ill-ordered base materials (i.e. one has a higher Young’s modulus, but lower thermal conductivity while another has a lower Young’s modulus but higher conductivity) are assumed in order to observe competition in the phase distribution defined by stiffness and conduction. The effective properties are derived from the homogenization method with periodic boundary conditions within a representative element (base cell). All the issues are transformed to the minimization problems subject to volume and symmetry constraints mathematically and solved by the method of moving asymptote (MMA), which is guided by the sensitivities with respect to the design variables. To regularize the problem the SIMP model is explored with the nonlinear diffusion techniques to create edge-preserving and checkerboard-free results. The illustrative examples show how to generate Pareto fronts by means of linear weighting functions, which provide an in-depth understanding how these objectives compete in the topologies.