Contents 2.5.3 Transient interlaminar thermal stresses 67 2.5.3.1 Transient temperature field 67 2.5.3.2 Thermal stress field 68 2.5.4 Transient in-plane thermal stresses 73 2.5.4.1 Transient temperature field 74 2.5.4.2 Thermal stress field 77 Strength of continuous-fiber composites 80 3.1 Introduction 80 3.2 Rule-of-mixtures 81 3.3 Stress concentrations due to fiber breakages 85 3.3.1 Static case 3.3.1.1 Single filament failure 5 3.3.1.2 Multi-filament failure 3.3.2 Dynamic case 94 3.4 Statistical tensile strength theories 98 3.4.1 Preliminary 98 3.4.2 Strength of individual fibers 102 3.4.3 Strength of fiber bundles 104 3.4.4 Correlations between single fiber and fiber bundle strengths 106 3.4.4.1 Analysis 106 3.4.4.2 Single fiber strength distribution 108 3.4.5 Experimental measurements of Weibull shape parameter 109 3.4.5.1 Single fiber tests 110 3.4.5.2 Loose bundle tests 113 3.4.6 Strength of unidirectional fiber composites 115 3.4.6.1 Equal load sharing 115 3.4.6.2 Idealized local load sharing 118 3.4.6.3 Monte-Carlo simulation 132 3.4.7 Strength of cross-ply composites 134 3.4.7.1 Energy absorption during multiple fracture 134 3.4.7.2 Transverse cracking of cross-ply laminates 136 3.4.7.3 Statistical analysis 145 3.4.7.4 Transverse cracking and Monte-Carlo simulation 150 3.4.8 Delamination in laminates of multi-directional plies 157Contents 2.5.3 Transient interlaminar thermal stresses 67 2.5.3.1 Transient temperature field 67 2.5.3.2 Thermal stress field 68 2.5.4 Transient in-plane thermal stresses 73 2.5.4.1 Transient temperature field 74 2.5.4.2 Thermal stress field 77 3 Strength of continuous-fiber composites 80 3.1 Introduction 80 3.2 Rule-of-mixtures 81 3.3 Stress concentrations due to fiber breakages 85 3.3.1 Static case 85 3.3.1.1 Single filament failure 85 3.3.1.2 Multi-filament failure 88 3.3.2 Dynamic case 94 3.4 Statistical tensile strength theories 98 3.4.1 Preliminary 98 3.4.2 Strength of individual fibers 102 3.4.3 Strength of fiber bundles 104 3.4.4 Correlations between single fiber and fiber bundle strengths 106 3.4.4.1 Analysis 106 3.4.4.2 Single fiber strength distribution 108 3.4.5 Experimental measurements of Weibull shape parameter 109 3.4.5.1 Single fiber tests 110 3.4.5.2 Loose bundle tests 113 3.4.6 Strength of unidirectional fiber composites 115 3.4.6.1 Equal load sharing 115 3.4.6.2 Idealized local load sharing 118 3.4.6.3 Monte-Carlo simulation 132 3.4.7 Strength of cross-ply composites 134 3.4.7.1 Energy absorption during multiple fracture 134 3.4.7.2 Transverse cracking of cross-ply laminates 136 3.4.7.3 Statistical analysis 145 3.4.7.4 Transverse cracking and Monte-Carlo simulation 150 3.4.8 Delamination in laminates of multi-directional plies 157