Chap-5. Plasticity Theory

8/16/2019 Chap-5. Plasticity Theory

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Plasticity

theory


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Introduction

• The study of yielding wasmotivated by the wish to

predict mechanical failure ofmaterials

• Yielding is considered as thebeginning of a process whichwill eventually lead to fracture


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STRESS FRACTURE

CRITERION• the simplest failure criterion is thatfailure is expected when the largestprincipal normal

stress reaches the uniaxial strength ofthe material.

• This approach is successful inpredicting fracture of brittle materialsunder tension-dominated loading


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MAXIMUM NORMAL

STRESS FRACTURE

CRITERION

the effective stress

the safety factor against fracture


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STRESS FRACTURE

CRITERION


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Yield Criteria

• A yield criterion is amathematical expression of thestress states that will causeyielding or Fracture.

• The most general form of ayield criterion is f!σx, σy, σz, τyz, τzx, τxy) = C

• For an isotropic materialf!"#$ "%$ "&' ( ) ( f (σ1, σ2, σ3)

e*ective stress is


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Yield Criteria

• Failure is not expected if is lessthan σ c:

< σ c

σ c is the materials property• Also$ the safety factor against failure is

+(


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Yield criterion for ductilematerial

• Instead of the rupture of atomicbonds$ the material is separated bysliding of atoms as shown


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Tresca criterion

• failure in ductile materials iscaused by shear deformations.

,o$ it is logical to establish ayield criterion in terms of theamount of shear stress a

material is able to sustain. This is the principle of the

Tresca theory


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Tresca (maximum sear

stress criterion!

• The simplest yield criterionis one rst proposed by

Tresca. It states thatyielding will occur when

the largest shear stressreaches a critical value.


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Tresca criterion

This yield criterion can be stated asfollows

The yield stress inshear


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,ample Problem

• A Plane ,tress element in a part made ofthe /#-T is found to have the followingstress

σx ( 0. 1si2 σy ( 3.3 1si$ and τxy ( 0./ 1si. The Axial Yield ,trength$ " Y$ of /#-T

aluminum is &0 1si$ and its ,hear Yield,tress$ τ Y$ is %/ 1si.

• Find Factor of ,afety using Tresca)riterion


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4on 5ises )riterion

Another yield criterion often used for ductile metals is theprediction that yielding occurs when the shear stress on the

octahedral planes reaches the critical value


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4on 5ises )riterion


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,ample Problem


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,ample Problem

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Chap-5. Plasticity Theory