444 Mechanics of Materials 2 where D is the ductility,defined in terms of the reduction in area r during a tensile test as D= 1-r The total strain range elastic plastic strain ranges i.e. △er=△ee+△ep the elastic range being given by Basquin's law △ee= 3.505.N012 E Under creep conditions the secondary creep rate s is given by the Arrhenius equation where H is the activation energy,R the universal gas constant,T the absolute temperature and Aa constant. Under increasing stress the power law equation gives the secondary creep rate as e9=Bo” with B and n both being constants. The latter two equations can then be combined to give The Larson-Miller parameter for life prediction under creep conditions is P1=T(logiot +C) The Sherby-Dorn parameter is P2 log1ofr-T and the Manson-Haferd parameter T-Ta P3= log10 tr -logio ta where tr=time to rupture and Ta and logio ta are the coordinates of the point at which graphs of T against logio tr converge.C and a are constants. For stress relaxation under constant strain 1.1 -T+BE(n 1)t 0h-1三 where o is the instantaneous stress,oi the initial stress,B and n the constants of the power law equation,E is Young's modulus and t the time interval. Griffith predicts that fracture will occur at a fracture stress of given by 2bEy o}= πa(1-v2) for plane strain444 Mechanics of Materials 2 where D is the ductility, defined in terms of the reduction in area r during a tensile test as D=1, (-) 1 1-r The total strain range = elastic + plastic strain ranges i.e. the elastic range being given by Basquin's law AS, = AE, + AE~ Under creep conditions the secondary creep rate E: is given by the Arrhenius equation E, 0 =Ae (-x) where H is the activation energy, R the universal gas constant, T the absolute temperature and A a constant. Under increasing stress the power law equation gives the secondary creep rate as &; = pa" with p and n both being constants. The latter two equations can then be combined to give E; = Ka"e (-k) The Larson -Miller parameter for life prediction under creep conditions is PI = T(log1, tr + C) The Sherby-Dorn parameter is a Pz = log,,tr - - T and the Manson-Haferd parameter where tr = time to rupture and T, and log,, t, are the coordinates of the point at which graphs of T against log,, tr converge. C and cx are constants. For stress relaxation under constant strain where a is the instantaneous stress, oi the initial stress, /? and n the constants of the power law equation, E is Young's modulus and t the time interval. Grifith predicts that fracture will occur at a fracture stress of given by 2bE y of 2 = for plane strain na(1 - U*)