Delaminations in composite structures: V.V. Bolotin D Longitudinal pressure: (a) scheme of loading: (6) boundary of bucklin 0.5 A number of more complicated problems were considered in the same manner, among them: initially ns previously subjected to the short-tit nal actional T=773 K buckled delaminations 3s, edge semi-elliptical delamina- and durations t=0. 15, 30, 60 and I 1-5, respectively) tions with secondary cracks", elliptical delaminations in shells*. etc. An illustrative elevated temperature, moisture and other environmental example is shown in Figure 18. A cylindrical laminated actions shell with an elliptical delamination situated near the Interlaminar fatigue of composites was studied internal surface is subjected to the longitudinal pressure. experimentally by a number of authors(see O'Brien The stability chart is drawn in the space of variables a, b Reifsnider"). The question arises how to present and E, where a and b are the semi-axes of th experimental results in the most rational and universal delamination, and Ex the nominal (membrane) strain form that allows the interpolation and extrapolation The surface ABC corresponds to the boundary of upon other loading levels, other initial crack sizes, etc. As buckling of the delamination that is assumed to be to the surface delaminations, the most sound approach is initially nonbuckled. The surface A'B'C corresponds to to use, as a controlling loading parameter, the range AG equations Ga=Ta and Gb=Tb, where indices a and b of the generalized driving force (in cyclic fatigue), or its relate to the semi-axes of the delamination both current magnitude G(in static fatigue) equations are satisfied on the line DB simultaneously Some results concerning graphite/epoxy, glass/epoxy, and organic fiber/epoxy composites subjected, before the cyclic loading, to a short-time-thermal action, were 7 GROWTH OF DELAMINATIONS DUE TO obtained by Bolotin et al.48-50. Figure 19 is obtained for FATIGUE the glass-textile/epoxy composite. There the interlami nar crack growth rate da/dN is plotted vs the range AG Delaminations in composite structures can grow both of the generalized driving force for specimens subjected under monotonous quasistatic loading and under cyclic to heating at 773 K Lines 1-5 correspond to increasing loading. They grow continuously, in a stable way when duration of thermal action up to 120 s The diagrams are the state of equilibrium(in the Griffith's sense) that is very similar to those for fatigue cracks in metals. The attained with the equality G;=r remains stable or at parameters of the lines, evidently, vary over a wide range least neutral during further growth. The growth will be A semi-theoretical equation jump-like, including that up to the complete splitting of a tructural component, when the attained state happens d4/4G-△G (16) to be unstable. The last situation is typical for most components under compression. was used to interpret these results. Material parameters The fatigue growth of delaminations is alike in many A, Gr, AGth, and r depend on the temperature and on the aspects to the fatigue crack growth in ordinary metal duration of thermal treatment. At gmax <<r the structures. Along with the proper (cyclic) fatigue, the exponent in equation(16) is m a 2. The remaining growth of delaminations also takes place under long- parameters can be estimated from the middle, Paris acting, sustained loading. This kind of damage, named Erdogan,'s part of the diagram. The estimates of Gr and here the static fatit typical for composites with AGuh in functions of T and t corresponding to Figure 19 polymer matrices as well as for composites subjected (b)are presented in Figure 137Delaminations in composite structures: V. V. Bolotin P A -~2b (a) (b) C i b/h B Figure 18 Cylindrical shell with an elliptical delamination under longitudinal pressure: (a) scheme of loading; (b) boundary of buckling (ABC) and that of growth (A'B'C') A number of more complicated problems were considered in the same manner, among them: initially buckled delaminations 35, edge semi-elliptical delamina￾tions with secondary cracks 41, elliptical delaminations in cylindrical 43'44 and spherical shells 45, etc. An illustrative example is shown in Figure 18. A cylindrical laminated shell with an elliptical delamination situated near the internal surface is subjected to the longitudinal pressure. The stability chart is drawn in the space of variables a, b and E~, where a and b are the semi-axes of the delamination, and e~ the nominal (membrane) strain. The surface ABC corresponds to the boundary of buckling of the delamination that is assumed to be initially nonbuckled. The surface A'B~C corresponds to equations G, = F, and Gb = Fb, where indices a and b relate to the semi-axes of the delamination. Both equations are satisfied on the line DB ~ simultaneously. 7 GROWTH OF DELAMINATIONS DUE TO FATIGUE Delaminations in composite structures can grow both under monotonous quasistatic loading and under cyclic loading. They grow continuously, in a stable way when the state of equilibrium (in the Griffith's sense) that is attained with the equality Gj = Fj remains stable or at 5 least neutral during further growth . The growth will be jump-like, including that up to the complete splitting of a structural component, when the attained state happens to be unstable. The last situation is typical for most components under compression. The fatigue growth of delaminations is alike in many aspects to the fatigue crack growth in ordinary metal structures. Along with the proper (cyclic) fatigue, the growth of delaminations also takes place under long￾acting, sustained loading. This kind of damage, named here the static fatigue, is typical for composites with polymer matrices as well as for composites subjected to dl mm (IN 'cycle 10-2 S ./.// 5 4 ./ o 10 -4 I I I I I 0.5 1 2 AG,~I2 Figure 19 Fatigue crack growth rate diagrams for composite speci￾mens previously subjected to the short-time thermal action at T = 773 K and durations t = 0, 15, 30, 60 and 120s (lines 1-5, respectively) elevated temperature, moisture and other environmental actions. Interlaminar fatigue of composites was studied experimentally by a number of authors (see O'Brien 46, Reifsnider47). The question arises how to present experimental results in the most rational and universal form that allows the interpolation and extrapolation upon other loading levels, other initial crack sizes, etc. As to the surface delaminations, the most sound approach is to use, as a controlling loading parameter, the range AG of the generalized driving force (in cyclic fatigue), or its current magnitude G (in static fatigue). Some results concerning graphite/epoxy, glass/epoxy, and organic fiber/epoxy composites subjected, before the cyclic loading, to a short-time-thermal action, were obtained by Bolotin et al. 48 50. Figure 19 is obtained for the glass-textile/epoxy composite. There the interlami￾nar crack growth rate da/dN is plotted vs the range AG of the generalized driving force for specimens subjected to heating at 773 K. Lines 1-5 correspond to increasing duration of thermal action up to 120 s. The diagrams are very similar to those for fatigue cracks in metals. The parameters of the lines, evidently, vary over a wide range. A semi-theoretical equation 35 --dNd° ~ A (AG~-~Gth-~m(1-~9~) Gf ) \ (16) was used to interpret these results. Material parameters A, Gf, AGth, and £ depend on the temperature and on the duration of thermal treatment. At Gma x << 1 ~ the exponent in equation (16) is m ~ 2. The remaining parameters can be estimated from the middle, Paris￾Erdogan's part of the diagram. The estimates of Gr and AGth in functions of T and t corresponding to Figure 19 (b) are presented in Figure 20. 137