italopersechino

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These are replies submitted by italopersechino

@mehdi jafari 

 

many thanks ;)

 

(I am a big noob)

@mehdi jafari 

I am sorry for not to be clear

It's simpler this way. Here is my problem:


NULL

restart:
with(linalg):
with(plots):
Digits:=15:

#E:=214000: sig_Y:=853: n:=0.0595: eps_f:=1.1005:
#R:=0.1: dK_th:=4.2: c:=-0.679: nu:=0.3: dK:=100:

P_str_fact:=1/(1-2*nu):

#pi:=3.141592654:

 

#Size of plastic zone at dK
PZc:=(1/((4*pi*P_str_fact^2)*(1+n)))*(dK/sig_Y)^2; #[m]

(1/4)*(1-2*nu)^2*dK^2/(pi*(1+n)*sig_Y^2)

(1)

#Size of plastic zone at dK=dK_th
x1:=(1/((4*pi*P_str_fact^2)*(1+n)))*(dK_th/sig_Y)^2; #[m]

(1/4)*(1-2*nu)^2*dK_th^2/(pi*(1+n)*sig_Y^2)

(2)

#Strain plastic amplitude along crack ligament (r)
deps:=(2*sig_Y/E)*(PZc/(r+x1))^(1/(1+n));

2*sig_Y*((1/4)*(1-2*nu)^2*dK^2/(pi*(1+n)*sig_Y^2*(r+(1/4)*(1-2*nu)^2*dK_th^2/(pi*(1+n)*sig_Y^2))))^(1/(1+n))/E

(3)

deps_tip:=subs(r=0,deps);

2*sig_Y*(dK^2/dK_th^2)^(1/(1+n))/E

(4)

deps_PZc:=subs(r=PZc-x1,deps);

2*sig_Y/E

(5)

 

 

#LCF
depsLCF:=2*eps_f*(2*Nf)^c;

2*eps_f*(2*Nf)^c

(6)

Nf:=1/Dam;

1/Dam

(7)

 

appo:=depsLCF=deps;

2*eps_f*(2/Dam)^c = 2*sig_Y*((1/4)*(1-2*nu)^2*dK^2/(pi*(1+n)*sig_Y^2*(r+(1/4)*(1-2*nu)^2*dK_th^2/(pi*(1+n)*sig_Y^2))))^(1/(1+n))/E

(8)

Damage:=solve(appo,Dam);

2*(sig_Y*(dK^2*(-1+2*nu)^2/(4*r*pi*sig_Y^2+4*r*pi*sig_Y^2*n+dK_th^2-4*dK_th^2*nu+4*dK_th^2*nu^2))^(1/(1+n))/(eps_f*E))^(-1/c)

(9)

``


I need an expression for the variable Damage in which there should be the variable PZc and x1.

Download Fatigue_crack_growth.mw

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