The application of classical fracture mechanics to laminated com posites is discussed. A convenient method is presented for predicting the static strength of a flawed specimen. Theoretical predictions are compared with experimental data for specimens containing two types of flaws.

This paper presents an analytical technique for determining the stress-strain response up to ultimate laminate failure for a laminated composite consisting of orthotropic lamina with nonlinear stress-strain behavior. The procedure, which has been programmed for a digital computer, will produce a laminate stress-strain curve up to ultimate failure. The technique is restricted to the prediction of ultimate strength for plane anisotropic laminates with midplane symmetry sub jected to biaxial membrane loads. Comparisons are made between analytical predictions and experimental results. The basic concepts of ultimate and limit strength design as applied to an advanced com posite structure are discussed.

An energy formulation and solutions are presented for the analysis of plane anisotropic rectangular plates with various boundary condi tions. The formulation includes linear theory stability analysis, the calculation of natural frequencies and mode shapes, and analysis of displacement due to lateral loads. In-plane loadings are included in all of these formulations. The Ritz technique is used to find the minimum of energy expressions using a series expansion of beam mode shape functions. Several numerical and experimental results are presented and compared.

A kinetic model is postulated which considers the interaction of cumulative fatigue damage and chance overload on a component or structure under typical probabilistic service load histories. This model recognizes that:[I] materials fail from pre-existing flaws; [2] that flaws develop in a characteristic manner which is determined by the material properties, state and magnitude of the stresses at the flaw perimeter, the history of the imposed tractions, the thermal and environmental histories; and [3] the critical load for structural failure is a decreasing function of the crack length.Since the growing crack may not be detected by inspection procedures before reaching critical proportions, the reliability of a component or structure must include the chance of survival with an undetected crack. Fundamental to this operation is the definition of a "critical load". Failure occurs when the resistance F(t) of an element or structure is decreased through flaw development to the level such that the next load at that level, the "critical load", will produce rapid fracture. The fatigue lifetime, an induced stochastic variable, is simply the time required to produce a sufficient strength degradation to permit failure.Let us assume that the damage rate accumulation may be approximated by a power-law growth equationwhere r is a positive exponent characteristic of material behavior and independent of test or service variables, and C is the dimension of the critical damage zone. The premultiplier M is proportional to the far field work inputed into the element by the service environment M = const. W r ~ ADrF 2r max and F is the load or stress, D is the effective compliance, and A is a constant. In addition assume that a "critical load" is correlated withwhere K is an apparent toughness or work parameter. Integrating (i) 465 Int Journ of Fracture Mech 8 (1972) 466 and employing (2) gives a statement for the time dependent residual strength F.(t) 2(r-l) = F.(to)2(r-l) --(r-l)A4F2rmax(t-t o) (3) 1 1 of the ith element in a population of N elements, where A 4 = ADrK 2(r-l) F(to) is the initial static strength of the component possessing a Weibull (extreme value) distributionwhere a and F(t ) are the shape and scale parameters, respectively, for the°Weibull ~istribution, and the distribution of some function G[F(to) ] = F(t) where statement (3) is required. Using (3) it is easily seen that the set of values where F(t) > F is the same as the set of values whereHence, the probability that F(t) > F is just the probability that (3') holds. Equation (4) gives this probability as P[F(t)>F] = P{F(to)>[F(t)2(r-1) P[F(t)>F] = exp I--] 1/2 (r-+ (r_l)A4F2rmax(t_to) i) } (5) F(t) (r-l) + (r-l)A4F2rmax(t-t o) ~f Fit2 (r-l) ] 1where a_ = a /2(r-l). Note that when t = t , (5) reduced to (4); that when t ~ t o ~he result that P[F(t) > 0] < l°is a positive probability that F(t) = 0; and that when F(t) > 0 the random variable F(t) 2(r-I) is distributed as a translated three parameter Weibull distribution as demonstrated in Figure i.In the experiment...

No abstract