MIL-HDBK-17-3E, Working Draft CHAPTER 4 DESIGN AND ANALYSIS Page 4.1 INTRODUCTION ....................................................................................................................... 4 4.2 BASIC LAMINA PROPERTIES AND MICROMECHANICS ...................................................... 4 4.2.1 Assumptions ...................................................................................................................... 5 4.2.1.1 Material homogeneity.............................................................................................. 5 4.2.1.2 Material orthotropy .................................................................................................. 5 4.2.1.3 Material linearity......................................................................................................5 4.2.1.4 Residual stresses.................................................................................................... 5 4.2.2 Fiber composites: physical properties ............................................................................... 5 4.2.2.1 Elastic properties .................................................................................................... 6 4.2.2.2 Viscoelastic properties .......................................................................................... 10 4.2.2.3 Thermal expansion and moisture swelling............................................................ 12 4.2.2.4 Thermal conduction and moisture diffusion .......................................................... 15 4.2.3 Fiber composites: strength and failure............................................................................. 16 4.2.3.1 Axial tensile strength............................................................................................. 16 4.2.3.1.1 Weakest link failure ................................................................................ 17 4.2.3.1.2 Cumulative weakening failure................................................................. 17 4.2.3.1.3 Fiber break propagation failure............................................................... 18 4.2.3.1.4 Cumulative group mode failure............................................................... 18 4.2.3.2 Axial compressive strength................................................................................... 18 4.2.3.3 Matrix mode strength ............................................................................................ 20 4.2.4 Strength under combined stress...................................................................................... 20 4.2.5 Summary ......................................................................................................................... 23 4.3 ANALYSIS OF LAMINATES .................................................................................................... 24 4.3.1 Lamina stress-strain relations.......................................................................................... 24 4.3.2 Lamination theory ............................................................................................................ 29 4.3.3 Laminate properties ......................................................................................................... 33 4.3.3.1 Membrane stresses .............................................................................................. 34 4.3.3.2 Bending.................................................................................................................36 4.3.3.3 Thermal expansion ............................................................................................... 40 4.3.3.4 Moisture expansion............................................................................................... 42 4.3.3.5 Conductivity .......................................................................................................... 43 4.3.4 Thermal and hygroscopic analysis .................................................................................. 43 4.3.4.1 Symmetric laminates............................................................................................. 45 4.3.4.2 Unsymmetric laminates......................................................................................... 45 4.3.5 Laminate stress analysis ................................................................................................. 46 4.3.5.1 Stresses due to mechanical loads ........................................................................ 46 4.3.5.2 Stresses due to temperature and moisture........................................................... 47 4.3.5.3 Netting analysis..................................................................................................... 48 4.3.5.3.1 Netting analysis for design of filament wound pressure vessels ............ 49 4.3.5.4 Interlaminar stresses............................................................................................. 51 4.3.5.5 Nonlinear stress analysis...................................................................................... 51 4.3.6 Summary ......................................................................................................................... 51 4.4 LAMINATE STRENGTH AND FAILURE ................................................................................. 52 4.4.1 Sequential ply failure approach........................................................................................ 53 4.4.1.1 Initial ply ................................................................................................................ 53 4.4.1.2 Subsequent failures .............................................................................................. 55 4.4.2 Fiber failure approach (laminate level failure).................................................................. 55 4-1 MIL-HDBK-17-3E, Working Draft 4.4.3 Laminate design............................................................................................................... 57 4.4.4 Stress concentrations ...................................................................................................... 58 4.4.5 Delamination.................................................................................................................... 61 4.4.5.1 Compression......................................................................................................... 63 4.4.6 Damage and failure modes.............................................................................................. 63 4.4.6.1 Tension .................................................................................................................63 4.4.6.1.1 Matrix cracks .......................................................................................... 64 4.4.6.2 Compression......................................................................................................... 66 4.4.7 Summary ......................................................................................................................... 67 4.5 COMPLEX LOADS .................................................................................................................. 67 4.5.1 Biaxial in-plane loads....................................................................................................... 67 4.5.2 Out-of-plane loads ........................................................................................................... 67 4.6 LAMINA TO LAMINATE CONSIDERATIONS ......................................................................... 67 4.6.1 Residual stresses and strains.......................................................................................... 67 4.6.2 Thickness effects............................................................................................................. 67 4.6.3 Edge effects..................................................................................................................... 68 4.6.4 Effects of transverse tensile properties in unidirectional tape.......................................... 69 4.6.5 Laminate stacking sequence effects................................................................................ 70 4.6.5.1 Introduction ........................................................................................................... 70 4.6.5.2 Design guidelines.................................................................................................. 71 4.6.5.2.1 Strong recommendations ....................................................................... 71 4.6.5.2.2 Recommendations.................................................................................. 72 4.6.6 Lamina-to-laminate statistics ........................................................................................... 73 4.6.7 Summary ......................................................................................................................... 73 4.7 COMPRESSIVE BUCKLING AND CRIPPLING ...................................................................... 73 4.7.1 Plate buckling and crippling ............................................................................................. 73 4.7.1.1 Introduction ........................................................................................................... 73 4.7.1.2 Initial buckling........................................................................................................74 4.7.1.3 Uniaxial loading - long plate with all sides simply supported