MIL-HDBK-17-3F Volume 3.Foreword Table of Contents 5.3.1 Lamina stress-strain relations.... 21 5.3.2 Lamination theory ................................ 27 5.3.3 Laminate properties… 31 5.3.3.1 Membrane stresses...... 31 5.3.3.2 Bending.............. 34 5.3.3.3 Thermal expansion.. ,37 5.3.3.4 Moisture expansion...... 40 5.3.3.5 Conductivity. 40 5.3.4 Thermal and hygroscopic analysis...... 41 5.3.4.1 Symmetric laminates42 5.3.4.2 Unsymmetric laminates. 43 5.3.5 Laminate stress analysis... 43 5.3.5.1 Stresses due to mechanical loads.... 43 5.3.5.2 Stresses due to temperature and moisture.............. 44 5.3.5.3 Netting analysis........ 45 5.3.5.3.1 Netting analysis for design of filament wound pressure vessels..........46 5.3.5.4 Interlaminar stresses..... 49 5.3.5.5 Nonlinear stress analysis...... 49 5.3.6 Summary......... 49 5.4 LAMINATE STRENGTH AND FAILURE.............. 50 5.4.1 Sequential ply failure approach. ,50 5.4.1.1 Initial ply..... 50 5.4.1.2 Subsequent failures.... 53 5.4.2 Fiber failure approach (laminate level failure).... .…53 5.4.3 Laminate design ............ 55 5.4.4 Stress concentrations.56 5.4.5 Delamination........ 59 5.4.5.1 Compression................ 60 5.4.6 Damage and failure modes...61 5.4.6.1 Tension... .....61 5.4.6.1.1 Matrix cracks......62 5.4.6.2 Compression.......... 63 5.4.7 Summary.… .64 5.5 COMPLER LOADS..............................................65 5.5.1 Biaxial in-plane loads 5 5.5.2 Out-of-plane loads........ 65 5.6 LAMINA TO LAMINATE CONSIDERATIONS...... 04165 5.6.1 Residual stresses and strains..65 5.6.2 Thickness effects.65 5.6.3 Edge effects........ 66 5.6.4 Effects of transverse tensile properties in unidirectional tape................................ 67 5.6.5 Laminate stacking sequence effects. 68 5.6.5.1lntr0 ductic0n........................68 5.6.5.2 Design guidelines.68 5.6.5.2.1 Strong recommendations.... 69 5.6.5.2.2 Recommendations.. 70 5.6.6 Lamina-to-laminate statistics.1 5.6.7 Summary...… ....71 5.7 COMPRESSIVE BUCKLING AND CRIPPLING...........71 5.7.1 Plate buckling and crippling...... 71 5.7.1.1 Introduction............... 71 5.7.1.2 7.1.2niti归buckling.s44444444444444…Z 5.7.1.3 Uniaxial loading-long plate with all sides simply supported 72 5.7.1.4 Uniaxial loading -long plate with all sides fixed ....................................7.4 5.7.1.5 Uniaxial loading-long plate with three sides simply supported and one unloaded edge free..75 viiiMIL-HDBK-17-3F Volume 3, Foreword / Table of Contents viii 5.3.1 Lamina stress-strain relations........................................................................................ 21 5.3.2 Lamination theory .......................................................................................................... 27 5.3.3 Laminate properties ....................................................................................................... 31 5.3.3.1 Membrane stresses ......................................................................................... 31 5.3.3.2 Bending............................................................................................................ 34 5.3.3.3 Thermal expansion .......................................................................................... 37 5.3.3.4 Moisture expansion.......................................................................................... 40 5.3.3.5 Conductivity ..................................................................................................... 40 5.3.4 Thermal and hygroscopic analysis ................................................................................ 41 5.3.4.1 Symmetric laminates ....................................................................................... 42 5.3.4.2 Unsymmetric laminates ................................................................................... 43 5.3.5 Laminate stress analysis ............................................................................................... 43 5.3.5.1 Stresses due to mechanical loads................................................................... 43 5.3.5.2 Stresses due to temperature and moisture ..................................................... 44 5.3.5.3 Netting analysis ............................................................................................... 45 5.3.5.3.1 Netting analysis for design of filament wound pressure vessels .......... 46 5.3.5.4 Interlaminar stresses ....................................................................................... 49 5.3.5.5 Nonlinear stress analysis................................................................................. 49 5.3.6 Summary........................................................................................................................ 49 5.4 LAMINATE STRENGTH AND FAILURE .................................................................................. 50 5.4.1 Sequential ply failure approach ..................................................................................... 50 5.4.1.1 Initial ply........................................................................................................... 50 5.4.1.2 Subsequent failures......................................................................................... 53 5.4.2 Fiber failure approach (laminate level failure) ............................................................... 53 5.4.3 Laminate design ............................................................................................................ 55 5.4.4 Stress concentrations .................................................................................................... 56 5.4.5 Delamination.................................................................................................................. 59 5.4.5.1 Compression.................................................................................................... 60 5.4.6 Damage and failure modes............................................................................................ 61 5.4.6.1 Tension ............................................................................................................ 61 5.4.6.1.1 Matrix cracks......................................................................................... 62 5.4.6.2 Compression.................................................................................................... 63 5.4.7 Summary........................................................................................................................ 64 5.5 COMPLEX LOADS .................................................................................................................. 65 5.5.1 Biaxial in-plane loads..................................................................................................... 65 5.5.2 Out-of-plane loads ......................................................................................................... 65 5.6 LAMINA TO LAMINATE CONSIDERATIONS .......................................................................... 65 5.6.1 Residual stresses and strains........................................................................................ 65 5.6.2 Thickness effects ........................................................................................................... 65 5.6.3 Edge effects................................................................................................................... 66 5.6.4 Effects of transverse tensile properties in unidirectional tape ....................................... 67 5.6.5 Laminate stacking sequence effects.............................................................................. 68 5.6.5.1 Introduction ...................................................................................................... 68 5.6.5.2 Design guidelines ............................................................................................ 68 5.6.5.2.1 Strong recommendations...................................................................... 69 5.6.5.2.2 Recommendations ................................................................................ 70 5.6.6 Lamina-to-laminate statistics ......................................................................................... 71 5.6.7 Summary........................................................................................................................ 71 5.7 COMPRESSIVE BUCKLING AND CRIPPLING ...................................................................... 71 5.7.1 Plate buckling and crippling........................................................................................... 71 5.7.1.1 Introduction ...................................................................................................... 71 5.7.1.2 Initial buckling .................................................................................................. 72 5.7.1.3 Uniaxial loading - long plate with all sides simply supported .......................... 72 5.7.1.4 Uniaxial loading - long plate with all sides fixed .............................................. 74 5.7.1.5 Uniaxial loading - long plate with three sides simply supported and one unloaded edge free............................................................................ 75