NOTATION Quanti的 Symbol SI Unit Angle a,B,日，y,中 rad (radian) Length L,s m (metre) mm (millimetre) Area A 2 Volume V m3 Time t s (second) Angular velocity ω rad/s Velocity U m/s Weight W N(newton) Mass m kg (kilogram) Density p kg/m3 Force F or P or W N Moment M Nm Pressure p Pa (Pascal) N/m2 bar(=105N/m2) Stress 0 N/m2 Strain Shear stress t N/m2 Shear strain y 一 Young's modulus E N/m2 Shear modulus G N/m2 Bulk modulus K N/m2 Poisson's ratio V Modular ratio m 二 Power W(watt) Coefficient of linear expansion a m/m'C Coefficient of friction L Second moment of area I m4 Polar moment of area J m4 Product moment of area I m4 Temperature T C Direction cosines I,m,n Principal stresses 01,02,03 N/m2 Principal strains E1,82,e3 Maximum shear stress Tmax N/m2 Octahedral stress Ooct N/m2 xvii
NOTATION Quantity Angle Length Area Volume Time Angular velocity Velocity Weight Mass Density Force Moment Pressure Stress Strain Shear stress Shear strain Young's modulus Shear modulus Bulk modulus Poisson's ratio Modular ratio Power Coefficient of linear expansion Coefficient of friction Second moment of area Polar moment of area Product moment of area Temperature Direction cosines Principal stresses Principal strains Maximum shear stress Octahedral stress A V t 0 2, W m P F or P or W M P (T E t Y E G K m V SI Unit rad (radian) m (metre) mm (millimetre) m2 m3 s (second) rad/s m/S N (newton) kg (kilogram) kg/m3 N Nm Pa (Pascal) N/m2 bar (= lo5 N/m2) N/m2 N/m2 N/m2 N/m2 N/m2 - - - W (watt) m/m"C m4 m4 m4 "C N/m2 N/m2 N/m2 - - - xvii
xviii Notation Quantity Symbol SI Unit Deviatoric stress 0 N/m2 Deviatoric strain E' Hydrostatic or mean stress 6 N/m2 Volumetric strain △ Stress concentration factor K Strain energy U J Displacement 8 m Deflection 8 or y m Radius of curvature p m Photoelastic material fringe value f N/m2/fringe/m Number of fringes 白 Body force stress X,Y,Z N/m3 FR,Fe,Fz Radius of gyration k m Slenderness ratio L/k Gravitational acceleration 8 m/s2 Cartesian coordinates x,y,Z Cylindrical coordinates r,8,2 -二 Eccentricity e m Number of coils or leaves of spring 之 - Equivalent J or effective polar moment of area JE m4 Autofrettage pressure N/m2 or bar Radius of elastic-plastic interface Rp m Thick cylinder radius ratio R2/R Ratio elastic-plastic interface radius to internal radius of thick cylinder Rp/R m Resultant stress on oblique plane Pn N/m2 Normal stress on oblique plane On N/m2 Shear stress on oblique plane Tn N/m2 Direction cosines of plane l,m,n Direction cosines of line of action of resultant stress I',m',n' - Direction cosines of line of action of shear stress ls,ms,ns Components of resultant stress on oblique plane Pxn,Pyn,Pin N/m2 Shear stress in any direction on oblique plane T中 N/m2 Invariants of stress N/m2 (N/m2)2 (N/m2)3 Invariants of reduced stresses J1,J2,J3 Airy stress function
xviii Notation Quantity Deviatoric stress Deviatoric strain Hydrostatic or mean stress Volumetric strain Stress concentration factor Strain energy Displacement Deflection Radius of curvature Photoelastic material fringe value Number of fringes Body force stress Radius of gyration Slenderness ratio Gravitational acceleration Cartesian coordinates Cylindrical coordinates Eccentricity Number of coils or leaves of spring Equivalent J or effective polar moment of area Autofrettage pressure Radius of elastic-plastic interface Thick cylinder radius ratio R2/R1 Ratio elastic-plastic interface radius to internal radius of thick cylinder R,/RI Resultant stress on oblique plane Normal stress on oblique plane Shear stress on oblique plane Direction cosines of plane Direction cosines of line of action of resultant stress Direction cosines of line of action of shear stress Components of resultant stress on oblique plane Shear stress in any direction 4 on oblique plane Invariants of stress Invariants of reduced stresses Airy stress function m l‘, m‘, n’ Pxn 9 Pyn 9 Pzn SI Unit N/m2 N/m2 - - - J m m m N/m2/fringe/m N/m3 - m4 N/m2 or bar m - N/m2 N/m2 N/m2 - N/m2 N/m2 N/m2 (N/m2)2 (N/m2)3
Notation Quantity Symbol SI Unit 'Operator'for Airy stress function biharmonic equation Strain rate s-1 Coefficient of viscosity 刀 Retardation time (creep strain recovery) s Relaxation time (creep stress relaxation) s Creep contraction or lateral strain ratio J() Maximum contact pressure (Hertz) Po N/m2 Contact formulae constant △ N/m2)-1 Contact area semi-axes a,b m Maximum contact stress 0c=-P0 N/m2 Spur gear contact formula constant K N/m2 Helical gear profile contact ratio mp Elastic stress concentration factor K Fatigue stress concentration factor Kf Plastic flow stress concentration factor Shear stress concentration factor Kts Endurance limit for n cycles of load Sn N/m2 Notch sensitivity factor 9 Fatigue notch factor - Strain concentration factor Ke Griffith's critical strain energy release Ge Surface energy of crack face Y Nm Plate thickness B m Strain energy U Nm Compliance C mN-I Fracture stress of N/m2 Stress Intensity Factor K or K N/m32 Compliance function Y Plastic zone dimension rp m Critical stress intensity factor KIC N/m3/2 “J'Integral J Fatigue crack dimension a m Coefficients of Paris Erdogan law C,m Fatigue stress range Or N/m2 Fatigue mean stress Om N/m2 Fatigue stress amplitude Oa N/m2 Fatigue stress ratio Rs Cycles to failure Nf 二 Fatigue strength for N cycles ON N/m2 Tensile strength OTS N/m2 Factor of safety F
Notation xix Quantity ‘Operator’ for Airy stress function biharmonic equation Strain rate Coefficient of viscosity Retardation time (creep strain recovery) Relaxation time (creep stress relaxation) Creep contraction or lateral strain ratio Maximum contact pressure (Hertz) Contact formulae constant Contact area semi-axes Maximum contact stress Spur gear contact formula constant Helical gear profile contact ratio Elastic stress concentration factor Fatigue stress concentration factor Plastic flow stress concentration factor Shear stress concentration factor Endurance limit for n cycles of load Notch sensitivity factor Fatigue notch factor Strain concentration factor Griffith’s critical strain energy release Surface energy of crack face Plate thickness Strain energy Compliance Fracture stress Stress Intensity Factor Compliance function Plastic zone dimension Critical stress intensity factor “J” Integral Fatigue crack dimension Coefficients of Paris Erdogan law Fatigue stress range Fatigue mean stress Fatigue stress amplitude Fatigue stress ratio Cycles to failure Fatigue strength for N cycles Tensile strength Factor of safety SI Unit S S - N/m2 (N/m2)-’ m N/m2 N/m2 - Nm m Nm mN-’ N/m2 N/m3I2 m N/m3I2 m N/m2 N/m2 N/m2 - - - N/m2 N/m2 -
XX Notation Quantiry Symbol SI Unit Elastic strain range AEe Plastic strain range AEp Total strain range △e, -- Ductility D Secondary creep rate s-1 Activation energy H Nm Universal Gas Constant R J/kgK Absolute temperature K Arrhenius equation constant A Larson-Miller creep parameter Pi Sherby-Dorn creep parameter P2 Manson-Haford creep parameter P3 Initial stress N/m2 Time to rupture tr Constants of power law equation B.n
xx Notation Quantity Elastic strain range Plastic strain range Total strain range Ductility Secondary creep rate Activation energy Universal Gas Constant Absolute temperature Arrhenius equation constant Larson-Miller creep parameter S herby - Dorn creep parameter Manson-Haford creep parameter Initial stress Time to rupture Constants of power law equation SI Unit - - S-' Nm JkgK "K - N/m2 S -