MIL-HDBK-17-3F Volume 3.Chapter 1 General Information m -(1)mass (kg,Ib) -(2)number of half wave lengths -(3)metre -(4)slope N -(1)number of fatigue cycles to failure -(2)number of laminae in a laminate -(3)distributed in-plane forces on a panel(Ibf/in) -(4)Newton -(5)normalized NA neutral axis n -(1)number of times in a set -(2)number of half or total wavelengths -(3)number of fatigue cycles endured -(1)applied load (N,Ibf) -(2)exposure parameter -(3)probability -(4)specific resistance() P test ultimate load,(N.Ib per fastener) py test yield load,(N,Ib per fastener) p normal pressure (Pa.psi) psi -pounds per square inch area static moment of a cross-section(mm3,in) shear flow(N/m,lbf/in) R -(1)algebraic ratio of minimum load to maximum load in cyclic loading -(2)reduced ratio RA reduction of area R.H. -relative humidity RMS root-mean-square RT room temperature -(1)radius(mm,in) -(2)root radius (mm,in) -(3)reduced ratio(regression analysis) -(1)shear force(N,Ibf) -(2)nominal stress in fatigue(MPa,ksi) -(3)S-basis for mechanical property values -stress amplitude in fatigue(MPa,ksi) e fatigue limit(MPa,ksi) Sm mean stress in fatigue(MPa,ksi) max -highest algebraic value of stress in the stress cycle(MPa,ksi) Smin lowest algebraic value of stress in the stress cycle(MPa,ksi) SR -algebraic difference between the minimum and maximum stresses in one cycle(MPa,ksi) S.F. safety factor -(1)arc length(mm,in) -(2)H/C sandwich cell size (mm,in) T -(1)temperature (C,F) -(2)applied torsional moment(N-m,in-Ibf) Ta thermal decomposition temperature(C,F) Tr exposure temperature (C,F) glass transition temperature (C,F) melting temperature (C,F) -(1)thickness (mm,in) -(2)exposure time (s) -(3)elapsed time (s) -(1)volume (mm,in) -(2)shear force (N,Ibf) 1-6
MIL-HDBK-17-3F Volume 3, Chapter 1 General Information 1-6 m - (1) mass (kg,lb) - (2) number of half wave lengths - (3) metre - (4) slope N - (1) number of fatigue cycles to failure - (2) number of laminae in a laminate - (3) distributed in-plane forces on a panel (lbf/in) - (4) Newton - (5) normalized NA - neutral axis n - (1) number of times in a set - (2) number of half or total wavelengths - (3) number of fatigue cycles endured P - (1) applied load (N,lbf) - (2) exposure parameter - (3) probability - (4) specific resistance (Ω) Pu - test ultimate load, (N,lb per fastener) Py - test yield load, (N,lb per fastener) p - normal pressure (Pa,psi) psi - pounds per square inch Q - area static moment of a cross-section (mm3 ,in3 ) q - shear flow (N/m,lbf/in) R - (1) algebraic ratio of minimum load to maximum load in cyclic loading - (2) reduced ratio RA - reduction of area R.H. - relative humidity RMS - root-mean-square RT - room temperature r - (1) radius (mm,in) - (2) root radius (mm,in) - (3) reduced ratio (regression analysis) S - (1) shear force (N,lbf) - (2) nominal stress in fatigue (MPa,ksi) - (3) S-basis for mechanical property values Sa - stress amplitude in fatigue (MPa,ksi) Se - fatigue limit (MPa,ksi) Sm - mean stress in fatigue (MPa,ksi) Smax - highest algebraic value of stress in the stress cycle (MPa,ksi) Smin - lowest algebraic value of stress in the stress cycle (MPa,ksi) SR - algebraic difference between the minimum and maximum stresses in one cycle (MPa,ksi) S.F. - safety factor s - (1) arc length (mm,in) - (2) H/C sandwich cell size (mm,in) T - (1) temperature (°C,°F) - (2) applied torsional moment (N-m,in-lbf) Td - thermal decomposition temperature (°C,°F) TF - exposure temperature (°C,°F) Tg - glass transition temperature (°C,°F) Tm - melting temperature (°C,°F) t - (1) thickness (mm,in) - (2) exposure time (s) - (3) elapsed time (s) V - (1) volume (mm3 ,in3 ) - (2) shear force (N,lbf)
MIL-HDBK-17-3F Volume 3.Chapter 1 General Information W -(1)weight (N,Ibf) -(2)width (mm,in) -(3)Watt -distance along a coordinate axis Y nondimensional factor relating component geometry and flaw size y -(1)deflection(due to bending)of elastic curve of a beam(mm,in) -(2)distance from neutral axis to given point -(3)distance along a coordinate axis Z -section modulus,I/y (mm,in) a -coefficient of thermal expansion(m/m/C,in/in/F) Y shear strain (m/m,in/in) △ -difference(used as prefix to quantitative symbols) d -elongation or deflection (mm.in) e strain(m/m,in/in) e elastic strain (m/m,in/in) -plastic strain(m/m,in/in) μ -permeability m -plasticity reduction factor [n] intrinsic viscosity n* -dynamic complex viscosity 2 -Poisson's ratio 0 -(1)density (kg/m3,lb/in3) -(2)radius of gyration(mm,in) Pc -H/C sandwich core density (kg/m,Ib/in total.summation 0 standard deviation 0,T前 stress in j direction on surface whose outer normal is in i direction (i,j =1,2,3 or x,y,z) (MPa,ksi) T -applied shear stress(MPa,ksi) 0 -angular velocity (radians/s) 09 infinity 1.3.1.1 Constituent properties The following symbols apply specifically to the constituent properties of a typical composite material. E -Young's modulus of filament material (MPa,ksi) Em -Young's modulus of matrix material(MPa,ksi) E发 -Young's modulus of impregnated glass scrim cloth in the filament direction or in the warp di- rection of a fabric(MPa,ksi) E明 -Young's modulus of impregnated glass scrim cloth transverse to the filament direction or to the warp direction in a fabric(MPa,ksi) G shear modulus of filament material(MPa,ksi) G -shear modulus of matrix(MPa,ksi) Gy -shear modulus of impregnated glass scrim cloth(MPa,ksi) Gex -shear modulus of sandwich core along X-axis(MPa,ksi) Gey -shear modulus of sandwich core along Y-axis(MPa,ksi) -filament length(mm,in) a -coefficient of thermal expansion for filament material(m/m/C,in/in/F) coefficient of thermal expansion for matrix material(m/m/C,in/in/F) 1-7
MIL-HDBK-17-3F Volume 3, Chapter 1 General Information 1-7 W - (1) weight (N,lbf) - (2) width (mm,in) - (3) Watt x - distance along a coordinate axis Y - nondimensional factor relating component geometry and flaw size y - (1) deflection (due to bending) of elastic curve of a beam (mm,in) - (2) distance from neutral axis to given point - (3) distance along a coordinate axis Z - section modulus, I/y (mm3 ,in3 ) α - coefficient of thermal expansion (m/m/°C,in/in/°F) γ - shear strain (m/m,in/in) ∆ - difference (used as prefix to quantitative symbols) δ - elongation or deflection (mm,in) ε - strain (m/m,in/in) ε e - elastic strain (m/m,in/in) ε p - plastic strain (m/m,in/in) µ - permeability η - plasticity reduction factor [η] - intrinsic viscosity η* - dynamic complex viscosity ν - Poisson's ratio ρ - (1) density (kg/m3,lb/in3) - (2) radius of gyration (mm,in) c ’ ρ - H/C sandwich core density (kg/m3 ,lb/in3 ) Σ - total, summation σ - standard deviation σij, τ ij - stress in j direction on surface whose outer normal is in i direction (i, j = 1, 2, 3 or x, y, z) (MPa,ksi) Τ - applied shear stress (MPa,ksi) ω - angular velocity (radians/s) ∞ - infinity 1.3.1.1 Constituent properties The following symbols apply specifically to the constituent properties of a typical composite material. Ef - Young's modulus of filament material (MPa,ksi) Em - Young's modulus of matrix material (MPa,ksi) x g E - Young's modulus of impregnated glass scrim cloth in the filament direction or in the warp direction of a fabric (MPa,ksi) y g E - Young's modulus of impregnated glass scrim cloth transverse to the filament direction or to the warp direction in a fabric (MPa,ksi) Gf - shear modulus of filament material (MPa,ksi) Gm - shear modulus of matrix (MPa,ksi) xy g G - shear modulus of impregnated glass scrim cloth (MPa,ksi) cx ’ G - shear modulus of sandwich core along X-axis (MPa,ksi) cy ’ G - shear modulus of sandwich core along Y-axis (MPa,ksi) A - filament length (mm,in) α f - coefficient of thermal expansion for filament material (m/m/°C,in/in/°F) α m - coefficient of thermal expansion for matrix material (m/m/°C,in/in/°F)
MIL-HDBK-17-3F Volume 3,Chapter 1 General Information a-coefficient of thermal expansion of impregnated glass scrim cloth in the filament direction or in the warp direction of a fabric(m/m/C,in/in/F) a-coefficient of thermal expansion of impregnated glass scrim cloth transverse to the filament di- rection or to the warp direction in a fabric(m/m/C,in/in/F) -Poisson's ratio of filament material vm -Poisson's ratio of matrix material v-glass scrim cloth Poisson's ratio relating to contraction in the transverse(or fill)direction as a result of extension in the longitudinal(or warp)direction -glass scrim cloth Poisson's ratio relating to contraction in the longitudinal(or warp)direction as a result of extension in the transverse (or fill)direction -applied axial stress at a point,as used in micromechanics analysis(MPa,ksi) 2 applied shear stress at a point,as used in micromechanics analysis(MPa,ksi) 1.3.1.2 Laminae and laminates The following symbols,abbreviations,and notations apply to composite laminae and laminates.At the present time the focus in MIL-HDBK-17 is on laminae properties.However,commonly used nomen- clature for both laminae and laminates are included here to avoid potential confusion. A(j=1,2,6) extensional rigidities (N/m,Ibf/in) B(i5=1,2,6) coupling matrix(N,Ibf) C(ij=1,2,6) elements of stiffness matrix(Pa,psi) D Dy flexural rigidities (N-m,Ibf-in) Dy -twisting rigidity (N-m,lbf-in) D(ij=1,2,6) flexural rigidities(N-m,Ibf-in) E -Young's modulus of lamina parallel to filament or warp direction(GPa,Msi) E2 -Young's modulus of lamina transverse to filament or warp direction(GPa,Msi) -Young's modulus of laminate along x reference axis(GPa,Msi) E Young's modulus of laminate along y reference axis(GPa,Msi) G12 shear modulus of lamina in 12 plane(GPa,Msi) Gxq -shear modulus of laminate in xy reference plane(GPa,Msi) h -thickness of it ply or lamina(mm,in) M,My,Mxy bending and twisting moment components(N-m/m,in-lbf/inin plate and shell analy- sis) 名 number of filaments per unit length per lamina Q Qy shear force parallel to z axis of sections of a plate perpendicular to x and y axes,re- spectively (N/m,Ibf/in) Q(j=1,2,6) reduced stiffness matrix(Pa,psi) Ux,Uy,Uz components of the displacement vector(mm,in) u哏，u9,u2 -components of the displacement vector at the laminate's midsurface(mm,in) V void content(%by volume) Vr -filament content or fiber volume(%by volume) Ve glass scrim cloth content(%by volume) Vm matrix content (by volume) Vx,Vy edge or support shear force(N/m,Ibf/in) Wr filament content(%by weight) Wg glass scrim cloth content(%by weight) m matrix content(%by weight) Ws weight of laminate per unit surface area(N/m2,lbf/in) Q1 -lamina coefficient of thermal expansion along 1 axis(m/m/C,in/in/F) Q2 lamina coefficient of thermal expansion along 2 axis(m/m/C,in/in/F) 1-8
MIL-HDBK-17-3F Volume 3, Chapter 1 General Information 1-8 x g α - coefficient of thermal expansion of impregnated glass scrim cloth in the filament direction or in the warp direction of a fabric (m/m/°C,in/in/°F) y g α - coefficient of thermal expansion of impregnated glass scrim cloth transverse to the filament direction or to the warp direction in a fabric (m/m/°C,in/in/°F) νf - Poisson's ratio of filament material ν m - Poisson's ratio of matrix material xy g ν - glass scrim cloth Poisson's ratio relating to contraction in the transverse (or fill) direction as a result of extension in the longitudinal (or warp) direction yx g ν - glass scrim cloth Poisson's ratio relating to contraction in the longitudinal (or warp) direction as a result of extension in the transverse (or fill) direction σ - applied axial stress at a point, as used in micromechanics analysis (MPa,ksi) τ - applied shear stress at a point, as used in micromechanics analysis (MPa,ksi) 1.3.1.2 Laminae and laminates The following symbols, abbreviations, and notations apply to composite laminae and laminates. At the present time the focus in MIL-HDBK-17 is on laminae properties. However, commonly used nomenclature for both laminae and laminates are included here to avoid potential confusion. Aij (i,j = 1,2,6) - extensional rigidities (N/m,lbf/in) Bij (i,j = 1,2,6) - coupling matrix (N,lbf) Cij (i,j = 1,2,6) - elements of stiffness matrix (Pa,psi) Dx, Dy - flexural rigidities (N-m,lbf-in) Dxy - twisting rigidity (N-m,lbf-in) Dij (i,j = 1,2,6) - flexural rigidities (N-m,lbf-in) E1 - Young's modulus of lamina parallel to filament or warp direction (GPa,Msi) E2 - Young's modulus of lamina transverse to filament or warp direction (GPa,Msi) Ex - Young's modulus of laminate along x reference axis (GPa,Msi) Ey - Young's modulus of laminate along y reference axis (GPa,Msi) G12 - shear modulus of lamina in 12 plane (GPa,Msi) Gxy - shear modulus of laminate in xy reference plane (GPa,Msi) hi - thickness of i th ply or lamina (mm,in) Mx, My, Mxy - bending and twisting moment components (N-m/m, in-lbf/in in plate and shell analysis) nf - number of filaments per unit length per lamina Qx, Qy - shear force parallel to z axis of sections of a plate perpendicular to x and y axes, respectively (N/m,lbf/in) Qij (i,j = 1,2,6) - reduced stiffness matrix (Pa,psi) ux, uy, uz - components of the displacement vector (mm,in) x o y o z o u , u , u - components of the displacement vector at the laminate's midsurface (mm,in) Vv - void content (% by volume) Vf - filament content or fiber volume (% by volume) Vg - glass scrim cloth content (% by volume) Vm - matrix content (% by volume) Vx, Vy - edge or support shear force (N/m,lbf/in) Wf - filament content (% by weight) Wg - glass scrim cloth content (% by weight) Wm - matrix content (% by weight) Ws - weight of laminate per unit surface area (N/m2 ,lbf/in2 ) α 1 - lamina coefficient of thermal expansion along 1 axis (m/m/°C,in/in/°F) α 2 - lamina coefficient of thermal expansion along 2 axis (m/m/°C,in/in/°F)
MIL-HDBK-17-3F Volume 3.Chapter 1 General Information ax laminate coefficient of thermal expansion along general reference x axis(m/m/C, in/in/F) y laminate coefficient of thermal expansion along general reference y axis(m/m/C, in/in/F) d xy laminate shear distortion coefficient of thermal expansion(m/m/C.in/in/F) -angular orientation of a lamina in a laminate,i.e.,angle between 1 and x axes() Axy -product of vxy and vyx V12 Poisson's ratio relating contraction in the 2 direction as a result of extension in the 1 direction V21 -Poisson's ratio relating contraction in the 1 direction as a result of extension in the 2 direction Vxy Poisson's ratio relating contraction in the y direction as a result of extension in the x direction Vyx Poisson's ratio relating contraction in the x direction as a result of extension in the y direction Pe -density of a single lamina(kg/m3,Ib/in3) Pe density of a laminate (kg/m3,lb/in -(1)general angular coordinate,( -(2)angle between x and load axes in off-axis loading ( 1.3.1.3 Subscripts The following subscript notations are considered standard in MIL-HDBK-17. 1,2,3 -laminae natural orthogonal coordinates(1 is filament or warp direction) A axial -(1)adhesive -(2)alternating app -apparent byp -bypass c composite system,specific filament/matrix composition.Composite as a whole,contrasted to individual constituents.Also,sandwich core when used in conjunction with prime ( -(4)critical CA centrifugal force e fatigue or endurance eff effective eq -equivalent filament 8 glass scrim cloth H -hoop i -ith position in a sequence L lateral m -(1)matrix -(2)mean max maximum min minimum -(1)nih(last)position in a sequence -(2)normal p -polar symmetric st stiffener T transverse iThe convention for Poisson's ratio should be checked before comparing different sources as different conventions are used. 1-9
MIL-HDBK-17-3F Volume 3, Chapter 1 General Information 1-9 α x - laminate coefficient of thermal expansion along general reference x axis (m/m/°C, in/in/°F) α y - laminate coefficient of thermal expansion along general reference y axis (m/m/°C, in/in/°F) α xy - laminate shear distortion coefficient of thermal expansion (m/m/°C,in/in/°F) θ - angular orientation of a lamina in a laminate, i.e., angle between 1 and x axes (°) λ xy - product of ν xy and ν yx ν 12 - Poisson's ratio relating contraction in the 2 direction as a result of extension in the 1 direction1 ν 21 - Poisson's ratio relating contraction in the 1 direction as a result of extension in the 2 direction1 ν xy - Poisson's ratio relating contraction in the y direction as a result of extension in the x direction1 ν yx - Poisson's ratio relating contraction in the x direction as a result of extension in the y direction1 ρ c - density of a single lamina (kg/m3 ,lb/in3 ) c ρ - density of a laminate (kg/m3 ,lb/in3 ) φ - (1) general angular coordinate, (°) - (2) angle between x and load axes in off-axis loading (°) 1.3.1.3 Subscripts The following subscript notations are considered standard in MIL-HDBK-17. 1, 2, 3 - laminae natural orthogonal coordinates (1 is filament or warp direction) A - axial a - (1) adhesive - (2) alternating app - apparent byp - bypass c - composite system, specific filament/matrix composition. Composite as a whole, contrasted to individual constituents. Also, sandwich core when used in conjunction with prime (') - (4) critical cf - centrifugal force e - fatigue or endurance eff - effective eq - equivalent f - filament g - glass scrim cloth H - hoop i - i th position in a sequence L - lateral m - (1) matrix - (2) mean max - maximum min - minimum n - (1) nth (last) position in a sequence - (2) normal p - polar s - symmetric st - stiffener T - transverse 1 The convention for Poisson’s ratio should be checked before comparing different sources as different conventions are used
MIL-HDBK-17-3F Volume 3.Chapter 1 General Information value of parameter at time t X,y,Z general coordinate system Σ total.or summation 0 initial or reference datum () format for indicating specific,temperature associated with term in parentheses.RT-room temperature(21C,70F);all other temperatures in F unless specified. 1.3.1.4 Superscripts The following superscript notations are considered standard in MIL-HDBK-17. b -bending br -bearing -(1)compression -(2)creep cc compressive crippling cr -compressive buckling e -elastic filament g glass scrim cloth IS interlaminar shear (i) -ith ply or lamina lim -limit,used to indicate limit loading m matrix ohc -open hole compression oht -open hole tension 0 -plastic pl -proportional limit rup rupture -shear scr -shear buckling sec -secant(modulus) SO offset shear T temperature or thermal t tension tan tangent(modulus) ultimate -yield -secondary(modulus),or denotes properties of H/C core when used with subscript c CAI compression after impact 1.3.1.5 Acronyms The following acronyms are used in MIL-HDBK-17. AA -atomic absorption AES Auger electron spectroscopy AIA -Aerospace Industries Association ANOVA analysis of variance ARL -US Army Research Laboratory ASTM -American Society for Testing and Materials BMI bismaleimide BVID -barely visible impact damage CAI compression after impact CCA composite cylinder assemblage CFRP carbon fiber reinforced plastic 1-10
MIL-HDBK-17-3F Volume 3, Chapter 1 General Information 1-10 t - value of parameter at time t x, y, z - general coordinate system ∑ - total, or summation o - initial or reference datum ( ) - format for indicating specific, temperature associated with term in parentheses. RT - room temperature (21°C,70°F); all other temperatures in °F unless specified. 1.3.1.4 Superscripts The following superscript notations are considered standard in MIL-HDBK-17. b - bending br - bearing c - (1) compression - (2) creep cc - compressive crippling cr - compressive buckling e - elastic f - filament g - glass scrim cloth is - interlaminar shear (i) - ith ply or lamina lim - limit, used to indicate limit loading m - matrix ohc - open hole compression oht - open hole tension p - plastic pl - proportional limit rup - rupture s - shear scr - shear buckling sec - secant (modulus) so - offset shear T - temperature or thermal t - tension tan - tangent (modulus) u - ultimate y - yield ' - secondary (modulus), or denotes properties of H/C core when used with subscript c CAI - compression after impact 1.3.1.5 Acronyms The following acronyms are used in MIL-HDBK-17. AA - atomic absorption AES - Auger electron spectroscopy AIA - Aerospace Industries Association ANOVA - analysis of variance ARL - US Army Research Laboratory ASTM - American Society for Testing and Materials BMI - bismaleimide BVID - barely visible impact damage CAI - compression after impact CCA - composite cylinder assemblage CFRP - carbon fiber reinforced plastic