CyclicPlasticity Flashcards
in Cycle plasticiy models, define Elasticity?|
Are uniquely determines by the strains. Hook’s law can be used to compute the magnitude of stresses for any set of strains INDEPENDENTLY ON THE PREVIOUS STRAIN HISTORY
in Cycle plasticiy models, define Plasticity?|
Stresses and strains during cyclic plasticity deformation ARE DEPENDENT ON THE PREVIOUS LOADING HISTORY.
Which are the major components of the Cyclic plasticity models
1) yield function
2) Flow rule
3) Hardening rule
What is a Yield Function?
- Is the first step of the CPlasticity
- Combination of stress that are needed to initiate plastic deformation (Von Mises or TResca)
Why for the Yield Function is used Von Mises?
- Is an elipse in Sigma1&Sigma2 that are the principal stresses-
- Sigma0 is the uniaxial elastic behaviour or Yield strenght.
- If im exceed the yield function that mean that i have plasticity (outside the elipse)
- Outside the Yield function i CANNOT use Hook’s law.
define the Von-Mises-Deviatoric Stress
is the Hypershpere
-In plasticity -> stress tensor as vector of 9-components
-[S] having normal stresses
-Elastic limit change (increase)
f= S:S-2K^2
Radius of the sphere will be (2K)^1/2 (square root of 2k)
and k= yield shear strenght uniaxial K=Sigma0/sqrt(3)
How can the Back stress is define?
- is the ALPHA
- the center of the yield function
- Never testing material will be alpha=0
- AFter aplication of the load yield function can mover alpha different from 0
- Apply stress to obtain deviatoric stress Sij (increment cycle plasticity model)
f = (S-alpha):(S-alpha)-2K^2 = 0
Mention the 2nd step of the Cyclic plasticity model.
Flow Rule
- (describe the relationship between the stresses and plastic strains during plastic deformation)
- is a constitutive equation, typically based on the normality postulates by Drucker.
n = Unit global vector in nomrmal direction
- Plasticity is postulated
- Increment in the plastic strain in normal direction
related to the 3th step, Hardening rule, what is the main objectives, and which are the 2 different alternatives.
- It describes how the yield surface is alterede due to plastic strain in order to fulfill the Consistency condition (during elastic-pastic deformation the stress state remains on the yield surface)
- New state of stress (ds+ds)
2 alternatives
- Isotropic hardening = Yield surface expand with plastic strain
- Kinematic hardening = Yield surface translates
What ISOTROPIC HARDENING?
- describes the increase inmaterial strength due to plastic strain
- elastic changing.
- radius increase and elastic limit increase due to plasticity
- Changing K in function of equivalent Strain
- Can predict transient behavior but cannot predict good response.
***Yield surface expands evenly in all directions during plastic deformation, with no change in shape and no translation of the yield surface center.
What KINEMATIC HARDENING?
- Predict the stress will increase during each loading cycle until deformation
- stress-controlled loading isotropic hardening predict elastic deformation after 1st cycle.
- Yield function remain the same.
- Center is moving.
- Elastic domain is 2 radius.
- Can predict stabilize behavior.
What is the main rule of the Hardening rule?
- REAL materials shows kinematic and isotropic hardening until stability after stabilization they shows just kinematic.
- If transient behavior is not our interest (fatigue analysis) cyclically stable material is assumed and only kinematic hardening rule.
Concistency condition?
Is requires that during elastic-plastic deformation the stress state remains on the yield surface
