Rokuro Muki

ON TRANSIENT THERMAL STRESSES IN VISCOELASTIC MATERIALS WITH TEMPERATURE-DEPENDENT PROPERTIES

Abstract : This paper deals with the quasi-static analysis of transient thermal stresses in the linear theory of homogeneous and isotropic viscoelastic solids with temperature-dependent physical characteristics. The underlying constitutive law rests on the temperature-time equivalence hypothesis according to which a uniform temperature change affects the viscoelastic response of the material through a corresponding uniform shift of the logarithmic time scale. If the temperature varies with time, the preceding hypothesis implies a dependence of the instantaneous stresses upon the entire temperature history. Following an exposition of the theoretical background, exact solutions are deduced to two specific problems. The first concerns the transient thermal stresses in a slab of infinite extent, generated by a temperature field that depends arbitrarily. (Author-PL).

ELASTOSTATIC LOAD-TRANSFER TO A HALF-SPACE FROM A PARTIALLY EMBEDDED AXIALLY LOADED ROD

Abstract This investigation is concerned with the diffusion of an axial load from a bar of arbitrary uniform cross-section that is immersed in, up to a finite depth, and bonded to a semi-infinite solid of distinct elastic properties. The bar is perpendicular to the plane boundary of the embedding medium. The determination of the desired resultant force in the submerged bar-segment is reduced to a Fredholm integral equation by means of an approximative scheme developed and tested earlier in connection with a more elementary three-dimensional load-transfer problem. Extensive numerical results illustrating the decay of the bar-force, appropriate to various choices of the governing geometric and material parameters, are presented for the particular case of a bar of circular cross-section.

Prediction of Flexural Fatigue Strength of CRFP Composites under Arbitrary Frequency, Stress Ratio and Temperature

This paper deals with fatigue strength of a class of CFRP laminates satisfying certain hypotheses and proposes a prediction method of the fatigue strength at an arbitrary combination of frequency, stress ratio and temperature. Three-point bending tests were conducted for satin-woven CFRP laminates T400/3601 under static, creep and fatigue loadings. The experimental data support the prediction method and the hypotheses.

On the Diffusion of an Axial Load from an Infinite Cylindrical Bar Embedded in an Elastic Medium

his investigation is concerned with the decay of the resultant axial force in an infinite cylindrical elastic bar that is completely bonded to an all around infinite elastic medium of distinct mechanical properties. The bar is subjected to an axial loading confined to, and uniformly distributed over, one of its cross-sections. First, a solution to this problem, exact within classical three-dimensional elastostatics, is obtained for the special case of a circular cylindrical bar. Next, an approximative solution scheme applicable to a cross-section of arbitrary shape is developed. This scheme is subsequently used to deduce an approximate solution for the bar of circular cross-section. The exact and the approximate solution appropriate to the circular bar are compared with each other, particular attention being given to their asymptotic behavior near the load and at large distances from the applied loading. The present work is preliminary to an approximate treatment of the physically more important problem pertaining to The diffusion of load from a transverse tension-bar that is immersed to a finite depth in an elastic halfspace. In addition, the results established here are of interest in connection with the study of fiber-reinforced materials.

Prediction of Tensile Fatigue Life for Unidirectional CFRP

Tensile fatigue strength in unidirectional CFRP depends on time and temperature as well as number of cycles. A prediction method of fatigue strength proposed [14] for polymer composites meeting certain conditions and confirmed for flexural fatigue strength of satin-woven CFRP laminates is applied to the tensile fatigue life of unidirectional CFRP. The method is based upon the four hypotheses: (A) same failure mechanisms for constant strain-rate (CSR), creep, and fatigue failure, (B) same time-temperature superposition principle for all failure strengths, (C) linear cumulative damage law for monotonic loading, and (D) linear dependence of fatigue strength upon stress ratio. Data are provided for tensile CSR, creep, and fatigue tests at various temperatures in the longitudinal direction of unidirectional CFRP. Experimental verification of the prediction method for the tensile fatigue strength of the unidirectional CFRP is presented.

Prediction of tensile fatigue life under temperature environment for unidirectional CFRP

A method for prediction of fatigue strength under temperature environment was proposed for polymer composites and its validity was confirmed for the flexural fatigue strength of satin-woven CFRP laminates and others. This method is based upon the four hypotheses: (A) same failure process under constant strain-rate (CSR), creep, and fatigue loadings, (B) same time-temperature superposition principle for all failure strengths, (C) linear cumulative damage law for a nondecreasing stress process, and (D) linear dependence of fatigue strength upon stress ratio. Data are provided for tensile CSR, creep, and fatigue tests at various loading rates, frequencies, and temperatures in the longitudinal direction of unidirectional CFRP. In this paper, experimental verification of the prediction method is discussed for the tensile fatigue strength of unidirectional CFRP.

Applicability of Fatigue Life Prediction Method to Polymer Composites

A prediction method of fatigue strength under an arbitraryfrequency, temperature, and stress ratio is proposed for polymercomposites and its validity is confirmed for the flexural fatiguestrength of satin-woven CFRP laminates. This method is based upon fourhypotheses: (a) same failure process under constant strain-rate (CSR),creep, and fatigue loadings, (b) same time-temperature superpositionprinciple for all failure strengths, (c) linear cumulative damage lawfor nondecreasing stress process, and (d) linear dependence of fatiguestrength upon stress ratio. This method was applied to the flexuralfatigue strength of various unidirectional CFRPs, and the verificationand limitations of this method were discussed.

Double cantilever beam models in adhesive mechanics

There is a growing need to accurately predict failure of adhesive joints. To meet this, mechanics researchers are turning to fracture mechanics [1]. Application of modern fracture mechanics to adhesive joints depends upon a stress analysis and characterization of the singular stress fields within the connection. In the application of fracture mechanics to crack propagation problems this poses only a moderate problem as there have been significant advances in the stress analysis of crack geometries. Unfortunately, the geometry associated with an adhesive joint such as a shear lap joint is extremely complicated. The adherends are flexible and the joint rotates, the adhesive layer has a finite thickness and possibly possesses non-linear and rate-dependent mechanical properties, while the adherend thickness may vary. The stress analysis problems are formidable. Some progress has been made by introducing simplifying assumptions and employing the two-dimensional theory of elasto-statics [2,3]. On the other hand, numerical methods such as finite elements[4] appear promising and, when properly employed, should prove useful. While both of these approaches are important and valuable, they are also difficult, time consuming and expensive. This difficulty in the stress analysis is proving to be a deterrent to the basic understanding of the physics and phenomena of adhesive joint failure. An interesting alternative is to use an approximate structural theory in the stress analysis. In this way it might be possible to extract much of the essential information without extensive mathematical or numerical work. In fact, the first stress analyses of adhesive joints [5-7] were done in this spirit although not with a fracture mechanics analysis as the prime goa\. In the case of an adhesive joint joining two slender members, it is particularly appealing to use plate or beam theories to simplify the stress analysis. For example, the use of simple beam theory by Gilman[8] proved quite useful in the understanding of the double cantilever beam test specimen. Subsequently the approximate predictions were refined by numerical and experimental methods [9-12] but the basic results presented in [8] are still valuable. A similar approach based upon a refined plate theory [13] was used in [14] to solve a related problem. A recent paper by Kanninen [15] has modified Gilmans analysis by approximately accounting for the thickness deformations in the beam. Suitable selection of a somewhat arbitrary parameter in Kanninens model has led to excellent agreement with established results [9-12]. Kanninens paper gives a good example of how an approximate structural theory can be successfully employed. As a long range goal it is desirable to develop an approximate but accurate structural theory for adhesive connections. Such a theory would permit approximate analysis of adhesive joints accounting for the effects of inelasticity, joint geometry, and bond line properties. The accuracy of such a theory must, of course, be assessed whenever possible by comparison with elasticity and experimental results. This paper is concerned with two alternative models of the double cantilever specimen and comparison of the responses predicted by the two models. In Section 2 we develop a solution to an idealized model of the double cantilever problem, the solution being exact within the framework of the geometric simplifications and the two dimensional elastostatic theory of plane

Stress distribution in a lap joint under tension-shear

Abstract This paper deals with the elastostatic load transfer of a tensile load in a model of an adhesive lap joint (tension-shear problem). The adhesive layer is regarded as infinitesimally thin and the displacement and traction vectors in the adherends are assumed to be continuous across the bond. The problem is reduced to a pair of Fredholm integral equations of the second kind which involve the mean angle between the deformed bond line and the tensile load. This angle, in turn, is determined by means of a scheme due to Goland and Reissner. Numerical results for the bond line stresses and the stress intensity factors at the ends of the bonded region are presented.

Time–Temperature Dependence of Tensile Strength of Unidirectional CFRP

We have observed in our previous works [Miyano, Y., Nakada, M., Kudoh, H. and Muki, R. (1999). Prediction of Tensile Fatigue Life under Temperature Environment for Unidirectional CFRP, Advanced Composite Materials, 8: 235–246; Miyano, Y., Nakada, M., Kudoh, H. and Muki, R. (1999). Determination of Tensile Fatigue Life of Unidirectional CFRP Specimen by Strand Tenting, Mechanics of Time-Dependent Materials, 4: 127–137] that the tensile strength along the longitudinal direction of unidirectional carbon fiber reinforced plastics (CFRP) is highly time–temperature dependent. In this paper, we propose a prediction scheme of the master curve for the tensile strength of CFRP under constant strain rate (CSR) loading; we extend Rosen’s analysis [Rosen,B.W. (1964). Tensile Failure of Fibrous Composites, AIAA J., 2: 1985–1994] for tensile failure of unidirectional fibrous composites with elastic matrix to CFRP with viscoelastic matrix by making two modifications. First, we replace the ineffective length with the recovery length over which the interfacial shear stress is uniform. Second, we substitute the value of shear relaxation modulus at the time of failure for shear modulus in Rosen’s formula after the first modification. The shear relaxation modulus of polymer in the CFRP was estimated from the tensile storage modulus of CFRP obtained from the dynamic double cantilever beam under various frequencies and temperatures. The tensile test for unidirectional CFRP was carried out at various loading rates and temperatures; a smooth curve was drawn to represent inherently scattered strength data for each temperature. The master curve for CFRP strength together with the shift factors was obtained. The predicted master curve for tensile strength using an assumed value 7.5 for Weibull shape parameter of fiber strength captured the test data for CFRP (T400 and Epikote 828) adequately for small to medium time but poorly for large time.