Akihiro Wada

Nowadays, fiber reinforced plastic (FRP) has been widely used in many areas such as auto mobile, airplane and marine vessel due to its high specific strength, good corrosion resistance, relatively low cost and so on. However, it still remains unknown that what kind of damage will happen in the internal structure when an automobile, which is made from FRP, has a slight impact with something such as a wall. Then the following road safety of the automobile cannot be guaranteed because certain parts may be exposed to damage in what seems even like a slight impact. In addition, it is well known that initial fracture can bring damage and great effect to the mechanical properties of the FRP material. The novelty of this paper is that the object of this research is micro crack such as transverse crack. While, almost previous report is aimed at delamination. Actually, before the delamination happens, micro crack has already occurred. The mechanical property of FRP is beginning to decrease by delamination. However, when the delamination occurred in the FRP is examined, it is already too late because the delamination can bring great influence to the safety of the FRP products. Therefore, it is important to investigate and detect the presence of micro crack with ultrasonic wave. In this way, some accidents might be avoided. While, because of the variety of the constraints in the fracture mechanism, the damage behavior is very difficult to evaluate and there are rarely researches and data on it. Although damage assessment by visual observation and the durable service life on FRP has become a general tendency in these recent years, the appropriate way of non-destructive examination has not been confirmed yet. The purpose of this study is to investigate the possibility of non-destructive examination with ultrasonic wave testing for mechanical damage of glass fiber reinforced plastics (GFRP). The possibility of dividing of Lamb wave modes by reducing the thickness of samples was confirmed and the variance of distribution of frequency of So mode wave by micro fracture in GFRP.

 A new single layer breakwater armour unit has been developed by Samsung C&T Corp., Chisui Corp., et al over the past two years. This development has been empirically tested and verified by running a drop test, as well as performing structural analysis and physical model tests. The structural and hydraulic stability has also been thoroughly verified. In addition, favourable results in terms of economics, environment and constructability have been gathered. Given this excellence, this new single layer armour unit is expected to be used for overseas bidding projects and execution sites around the world including Japan.

A new technique using Lamb waves has been proposed to detect impact damages in FRP laminates nondestructively. Conventional ultrasonic testing such as C-scan requires two-dimensional scanning for whole area inspection because the inspected area by one operation is relatively small. In this study, for quick detection of a localized defect, spectrum analysis of Lamb waves is demonstrated. Instead of wave velocity or attenuation, acousto-ultrasonic parameters (AU parameters), which are based on the amplitude spectrum of the broadband signal, are introduced to improve the precision of the inspection. Among the several AU parameters, A2 and A4/A3 parameters, which represent the centroid and the torsion of the spectral density curve respectively, are found to be more useful to identify a localized defect in laminated composite plates. It is also found that the inspection accuracy depends on the wave propagation direction reflecting to the scattering of higher frequency waves, and can be improved by use of burst waves. © 2012 The Japan Society of Mechanical Engineers.

In this study, partially debonded spherical particles in a particulate composite are analyzed by three-dimensional finite element method to investigate the effect of debondings on the composite stiffness, and the way to replace a debonded particle with an equivalent inclusion is examined. The variation in Young's modulus and Poisson's ratio of a composite with the increase of the debonded angle was evaluated for different particle arrangements and particle volume fractions, which in turn compared with the results derived from the equivalent inclusion method. Consequently, it was found that by replacing a debonded particle with an equivalent othotropic one, the macroscopic behavior of the damaged composite could be reproduced so long as the interaction between neighboring particles is negligible.

A temperature-insensitive damage evaluation parameter for composite laminates is proposed. Ultrasonic wave velocity is directly related to material stiffness, so that it is a quantitative parameter that gives information about the mechanical state of the material. However, ultrasonic velocities vary with temperature therefore environmental factors might cause non-negligible error in inspected results. In this work, the angular dependence of Lamb wave propagation, i.e., the acoustic anisotropy, is exclusively focused on and the change in the acoustic anisotropy is used as a damage evaluation parameter. It is experimentally confirmed that the acoustic anisotropy is significantly altered by matrix cracks formation although it is insensitive to temperature variation. It is also shown that the combination of different Lamb modes is a more promising method for predicting the effective stiffness of damaged laminates.

An analytical model for FRP crossply laminates subjected to a bending load is developed in the framework of continuum damage mechanics. Constitutive equations for a cracked ply are firstly formulated under an assumption of equivalence between a cracked ply and a work-softening material. After dividing a laminated beam into small beam elements, the derived constitutive equations for a cracked ply are introduced into the lamination theory to predict the damage evolution in the laminated beam with a cracked ply. Each beam element is analyzed independently to compute the stress state and curvature of the element, and they are reconnected with each other to predict the deflection of the overall laminate beam. Two kinds of crossply laminate beams having different cracked ply thickness were tested in bending, and corresponding theoretical predictions were made. The prediction for crack distribution as well as load-displacement relations were in good agreement with the experimental results for each laminate.

An analytical model to predict the constitutive behavior of laminated composites with cracking layers is developed in the framework of continuum damage mechanics. A new concept that a cracked lamina can be replaced with: an equivalent uniform work-softening layer is proposed. With this new concept, the constitutive equations for a cracking layer are constructed according to the modern plasticity theory. A lamina damage surface, a threshold of crack evolution, is defined in the stress space, and the constitutive equations for a cracking layer are constructed along with the associated flow rule. Furthermore, the derived constitutive equations for a Cracking layer are applied to the classical lamination theory to describe laminate constitutive behavior in the cracking process The validity of the constitutive model formulation is also verified comparing the analytical predictions to experimental results for some laminate configurations.

An analytical model to predict the constitutive behavior of laminated composites with cracking layers is developed in the framework of continuum damage mechanics. A new concept that a cracked lamina can be replaced with an equivalent uniform work-softening layer is proposed. With this new concept, the constitutive equations for a cracking layer are constructed according to the modem plasticity theory. A lamina damage surface, a threshold of crack evolution, is defined in the stress space, and the constitutive equations for a cracking layer are constructed along with the associated flow rule. Furthermore, the derived constitutive equations for a cracking layer are applied to the classical lamination theory to describe laminate constitutive behavior in cracking process. The validity of the constitutive model formulation is also verified comparing the analytical predictions to experimental results for some laminate configurations.

An analytical model for predicting the matrix crack induced stiffness reduction of FRP laminates with off-axis cracked plies is developed. The constitutive equations for a cracking ply are first proposed with the assumption of the equivalence between a cracking ply and a work-softening material. Then they are incorporated into the classical lamination theory to describe the damage evolution in FRP laminates with off-axis cracked plies. The energy release rate in a cracking ply is adopted as the criterion for crack formation, and the number of cracks is predicted by dividing the cumulative released energy in a cracked ply by the released energy due to single crack formation. With the predicted number of cracks, the variation of the laminate stiffness with the crack density is evaluated. The uniaxial tension test is performed on GFRP [0/θn/0] laminates, and the elastic modulus in the loading direction is measured at five different crack density. The experimental results are compared to the corresponding predictions of the elastic modulus for three different center ply angles.

A damage mechanics model to predict the nonlinear behavior of laminated composites due to crack evolution is developed. We propose a new concept that a cracking layer can be replaced with an equivalent uniform work-softening layer. With this new concept, the constitutive equations for a cracking layer are constructed according to modern plasticity theory. A lamina damage surface, i.e. a threshold of crack evolution, is defined in the stress space of each lamina, and the constitutive equations for a cracking layer are constructed by applying the defined damage surface to the associated flow rule. Then, the derived constitutive equations for a cracking layer are introduced with classical lamination theory to predict laminate constitutive behavior in the damage process. Comparisons are made between the predictions and experimental results for some laminate configurations, and reasonable agreements are shown for all laminates.

In loading process of FRP laminates, two kinds of nonlinearity are observed. One of them is concerned with damage, the other is not. The nonlinearity unrelated with damage is mostly due to the nonlinear property of lamina in shear. On the other hand, the nonlinearity related with damage is caused by matrix cracking evolution in each ply. In the previous works, we presented the theory for predicting a laminate stress-strain response in damage process on the basis of continuum damage mechanics. This paper extends the theory to include the damage unrelated nonlinearity using Hahn & Tsai nonlinear elasticity theory. Comparisons are made between the analytical predictions and the experimental results. The analytical method formulated in this paper can be used for general composite laminates under the plane stress condition.

In Part I of this study, the constitutive equation of a cracking layer was formulated introducing the new concept that a cracked lamina was replaced by an equivalent uniform work-softening layer. Part II formulates laminate constitutive equation in damage process using the results obtained in Part I and the laminate theory. In this formulation, influence of lamina stacking sequence is discussed through the magnification of an initial damage surface. It is shown that the damage evolution law in Part I can be used for general laminates even if the initial damage surface is enlarged, as long as cracking layer energy release rate is adopted as a cracking criterion. Present model is shown to reproduce experimental results with good accuracy. Finally, discussions about laminate stiffness reduction and stress path in damage process are given.

Matrix cracking evolution in composite laminates is formulated in the framework of the continuum damage mechanics. In this paper, the damage evolution of a cracking layer is exclusively focused on. We propose a new concept that a cracked lamina is replaced by an equivalent uniform worksoftening layer, and the analytical method of plasticity is introduced to describe the behavior of the work-softening layer. The most important element of this model is a definition of work-softening modulus which is concerned with the damage evolution law. The elastic analysis proposed by Hashin is shown to be available for formulation of the damage evolution law, and it is also shown that adoption of the cracking layer energy release rate as a cracking criterion leads to a reasonable damage evolution law. The model formulated in this paper can be used for general composite laminates.