东南大学：《固体力学基础》课程教学课件（英文讲稿）08 Metal Plasticity

Metal Plasticitymi@se.ed.cn

Metal Plasticity

OutlineIntroduction（引言）·1D plasticity theory（一维塑性）·Roughvaluesofyieldstress（常用工程材料屈服应力值）·3Dplasticitytheory（三维塑性理论）·Decompositionof strain（应变分解）·Yield criterion（屈服判据）·Yield surface（屈服面）·Isotropic strainhardening（各向同性强化）·Kinematic strain hardening（运动强化）·Principalofmaximumplasticresistance（最大塑阻原理）·Lawofplasticflow（塑性流动定律）·Elastic unloadingconditions（弹性卸载的条件）2

Outline • Introduction（引言） • 1D plasticity theory（一维塑性） • Rough values of yield stress（常用工程材料屈服应力值） • 3D plasticity theory（三维塑性理论） • Decomposition of strain（应变分解） • Yield criterion（屈服判据） • Yield surface（屈服面） • Isotropic strain hardening（各向同性强化） • Kinematic strain hardening（运动强化） • Principal of maximum plastic resistance（最大塑阻原理） • Law of plastic flow（塑性流动定律） • Elastic unloading conditions（弹性卸载的条件） 2

Lntroduction. Linear elastic first: Plastic (permanent deformation); Unloadingfollows linear curve; Relaxation; Creep; Bauschinger effect; Cyclichardening/softening, Rate, loading history and temperatureHold atdependentconstant stressStressHoldatconstantstrainLinearUnloadingelasticStrainPermanentstrain3

• Linear elastic first; Plastic (permanent deformation); Unloading follows linear curve; Relaxation; Creep; Bauschinger effect; Cyclic hardening/softening; Rate, loading history and temperature dependent Introduction 3

Lntroduction.In 1930's,Taylorand scientists experimentallymeasured theresponseofthin-walled tubes under combined torsion, axial loading, and hydrostatic pressure.: Hydrostatic stress has no effects on plastic deformation..Plastic behavior doesn't induce volume change of a material.: Plastic deformation is caused by shearing of atomic planes via propagation of atype of lattice defects called dislocations.: During plastic loading, the principal components of the plastic strain rate tensorare parallel to the components of stress acting on the solid.Levy-Mises flow rule relates the principal plastic strain increment to theprincipal stresses.def - delldep -deidel-dspC,-0u-d1C-Omdislocation4

• In 1930’s, Taylor and scientists experimentally measured the response of thin￾walled tubes under combined torsion, axial loading, and hydrostatic pressure. • Hydrostatic stress has no effects on plastic deformation. • Plastic behavior doesn’t induce volume change of a material. • Plastic deformation is caused by shearing of atomic planes via propagation of a type of lattice defects called dislocations. • During plastic loading, the principal components of the plastic strain rate tensor are parallel to the components of stress acting on the solid. • Levy–Mises flow rule relates the principal plastic strain increment to the principal stresses. Introduction 4 p p p p p p I II II III III I I II II III III I d d d d d d                    

Introduction: Decomposition of strain, yield criteria, strain hardeningrules, plastic flow rule, elastic unloading criterion. We restrict attention to small deformations (≤10%)9,80OmetalQyoEECo1 &pE5

• Decomposition of strain, yield criteria, strain hardening rules, plastic flow rule, elastic unloading criterion • We restrict attention to small deformations (≤10%). Introduction 5

1D Plasticity. Decomposition of strain: de= dee +dep, do= Edee6. Yield criterion: =o[eP? Strain hardening rules govern thefunctional dependence of yield stressePaeon plastic strain.VRigid-perfectly plastic model0Oy =const.OH86

• Decomposition of strain: 1D Plasticity 6 , e p e d d d d Ed         • Yield criterion: p    Y      • Strain hardening rules govern the functional dependence of yield stress on plastic strain. Rigid-perfectly plastic model const. Y 

1D PlasticityVElastic-perfectly plastic model0Oy=constOH8VLinear hardening modelQyo'<QyoEEOPα≥OyoCOE-EEaElFOyoE-EE87

1D Plasticity 7 Elastic-perfectly plastic model const. Y  Linear hardening model 0 0 1 0 0 1 , , Y Y Y p Y Y Y EE E E                    

1D PlasticityaVPower law hardening modelQyQyo6<Oyo0YO:NHzOyoOvol8E6p. Here Oyo, E, and N can be treated as fitting parameters toexperimental data. O≤N<1 is called the hardening index. Tangent modulus of the stress-plastic strain curveN-1dgESTEN1de8

1D Plasticity 8 Power law hardening model 0 0 0 0 0 , 1 , Y Y N p Y Y Y Y E                         • Here σY0 , E, and N can be treated as fitting parameters to experimental data. 0≤N<1 is called the hardening index. • Tangent modulus of the stress-plastic strain curve 1 0 1 N P P Y d E h EN d              

1D Plasticity. Law of plastic flow:dgdade=de+depα=oy,do>0EhQyoTh1OyoQyoH8h=0h = constOyoa. Elastic unloading condition:QyOyoodg<0E8019SE6p

1D Plasticity 9 • Law of plastic flow: , , 0 e p Y d d d d d d E h               h  0 h  const 0 0 1 N P Y Y Y E            • Elastic unloading condition:  d  0

Rough Values of Yield StressMaterialYieldStressO,/MNm-2MaterialYieldStressOy/MNm-26000220Mild steelTungsten carbide6010000Silicon carbideCopper2000TungstenTitanium180-1320Alumina5000Silica glass7200400040-200Titanium carbideAluminumandalloys800052-90Silicon nitridePolyimidesNickel70Nylon498750IronPMMA60-11055Low alloy steels500-1980PolycarbonatePVC4548Stainless steel286-50010

Rough Values of Yield Stress 10