Casting simulation method

Abstract

Provided is a casting simulation method capable of expressing influence of different inelastic strains produced at different temperatures on strain hardenability at room temperature. The following amount of effective equivalent inelastic strain ε effective inelastic is substituted into a constitutive equation in which an amount of equivalent inelastic strain is used as a degree of work hardening: an amount of effective equivalent inelastic strain ε effective inelastic =∫ o t {h (T) /h (RT) }{(Δε inelastic /Δt )} dt , where T denotes a temperature with inelastic strain, h (T) denotes an increment of yield strength at room temperature with respect to an amount of inelastic strain at the temperature with inelastic strain, h (RT) denotes an increment of yield strength at room temperature with respect to an amount of inelastic strain applied at room temperature, h (T) /h (RT) denotes an effective inelastic strain coefficient α(T), Δε inelastic /Δt denotes an equivalent inelastic strain rate, and t denotes a time from 0 second in analysis.

1 . A casting simulation method capable of expressing influence of different inelastic strains produced at different temperatures on work hardening, namely on increase in yield stress, at room temperature, the influence varying with differences in recovery at the different temperatures, by introducing an amount of effective equivalent inelastic strain to an elasto-plastic constitutive equation and/or an elasto-viscoplastic constitutive equation in which an amount of equivalent inelastic strain is used as a degree of work hardening, namely an amount of increase in yield stress, such as an elasto-plastic constitutive equation in which a yield function is expressed as f=f(σ eff ,ε eff   p ,T) or an elasto-viscoplastic constitutive equation in which a relation between equivalent stress, equivalent viscoplastic strain, viscoplastic strain rate, and temperature is expressed as σ eff. =F(ε eff.   vp ,{dot over (ε)} eff.   vp ,T), wherein
 an amount of effective equivalent inelastic strain ε effective inelastic  obtained by Eq. (1) below is used:
   the amount of effective equivalent inelastic strain ε effective inelastic =∫ o   t   {h   (T)   /h   (RT) }{(Δε inelastic   /Δt )} dt    (1)
 
 
 
       , where
 T denotes a temperature with inelastic strain, 
 h (T)  denotes an increment of yield strength at room temperature with respect to an amount of inelastic strain at the temperature with inelastic strain, 
 h (RT)  denotes an increment of yield strength at room temperature with respect to an amount of inelastic strain applied at room temperature, 
 h (T) /h (RT)  denotes an effective inelastic strain coefficient α(T), 
 Δε inelastic /Δt denotes an equivalent inelastic strain rate, and 
 t denotes a time from 0 second in analysis. 
 
     
     
         2 . The casting simulation method according to  claim 1 , the effective inelastic strain coefficient α(T) is obtained by: applying different inelastic pre-strains to a test piece at different temperatures; cooling the test piece to room temperature; performing a tensile test or a compression test on the test piece at room temperature; and measuring influence of amounts of the inelastic pre-strains applied at the different temperatures on the increase in yield stress. 
     
     
         3 . The casting simulation method according to  claim 1 , wherein a stress-equivalent inelastic strain curve is transformed into a stress-effective equivalent inelastic strain curve using α(T), and based on the stress-effective equivalent inelastic strain curve, a determination is made of a material constant in a constitutive equation to which the amount of effective equivalent inelastic strain ε effective inelastic  is introduced. 
     
     
         4 . The casting simulation method according to  claim 1 , wherein when α(T) is substituted into Eq. (1) in a temperature range in which α(T) is 0 or a negative value and a stress-equivalent inelastic strain curve at the temperature T indicates work hardening, α(T) is corrected from 0 or the negative value to a small positive value. 
     
     
         5 . The casting simulation method according to  claim 2 , wherein a stress-equivalent inelastic strain curve is transformed into a stress-effective equivalent inelastic strain curve using α(T), and based on the stress-effective equivalent inelastic strain curve, a determination is made of a material constant in a constitutive equation to which the amount of effective equivalent inelastic strain ε effective inelastic  is introduced. 
     
     
         6 . The casting simulation method according to  claim 2 , wherein when α(T) is substituted into Eq. (1) in a temperature range in which α(T) is 0 or a negative value and a stress-equivalent inelastic strain curve at the temperature T indicates work hardening, α(T) is corrected from 0 or the negative value to a small positive value. 
     
     
         7 . The casting simulation method according to  claim 3 , wherein when α(T) is substituted into Eq. (1) in a temperature range in which α(T) is 0 or a negative value and a stress-equivalent inelastic strain curve at the temperature T indicates work hardening, α(T) is corrected from 0 or the negative value to a small positive value. 
     
     
         8 . The casting simulation method according to  claim 5 , wherein when α(T) is substituted into Eq. (1) in a temperature range in which α(T) is 0 or a negative value and a stress-equivalent inelastic strain curve at the temperature T indicates work hardening, α(T) is corrected from 0 or the negative value to a small positive value.