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7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 19
Metal Forming ampMachining
MF C314
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 29
Theory of Slip Lines Upper andLower Bound Theorem
Derivation of basic equations for solution of elastic-plasticdeformation
These are mentioned below along with boundaryconditions
I Equations of equilibriumII Compatibility equations
III Yield conditions
IV Stress-strain relations
V Strain-displacement relationsVI Incompressibility condition for plastic strains
VII Boundary conditions in stresses or displacements ormixed
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 39
The stress-strain relations in plasticity are non-linear
Yield condition in case of Von-Misesrsquo is also non-
linear Therefore it is not easy to solve these equations
without some approximations and simplifications of
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 49
Various difficulties in metal forming In many metal forming problems the boundary
stresses are unknown
As the plastic deformation proceeds the materialproperties go on changing due to strain hardening
At high rate of plastic deformation the temperature
o e e orm ng o y ncreases apprec a y w calso change the material properties
Phase change may take place during plasticdeformation which can also change the strength of
the metal body The nature of interfacial friction between tool and
metal is seldom known exactly
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 59
Different methods for solution Slab method
Slip line method Upper Bound method
Lower Bound method
Numerical techniques and Finite Element Method
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 69
Slab Method Plain sections remain plane during compression
Any non-uniformity in deformation is neglected Material is rigid perfectly plastic
Effects of strain hardening and strain rate are
neglected Method will be discussed later in details
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 79
983124983144983141983151983154983161 983151983142 983123983148983145983152 983116983145983150983141
Lines of maximum shear stress called slip lines
Slip lines are directions of maximum shear stressin the body undergoing plastic deformation
For plane strain deformation equilibrium equations
and yield condition (von Mises or Tresca) arerequired
Partial differential equations along with yield
condition in plain strain are hyperbolic partialdifferential equations
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 89
983096
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 99
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 29
Theory of Slip Lines Upper andLower Bound Theorem
Derivation of basic equations for solution of elastic-plasticdeformation
These are mentioned below along with boundaryconditions
I Equations of equilibriumII Compatibility equations
III Yield conditions
IV Stress-strain relations
V Strain-displacement relationsVI Incompressibility condition for plastic strains
VII Boundary conditions in stresses or displacements ormixed
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 39
The stress-strain relations in plasticity are non-linear
Yield condition in case of Von-Misesrsquo is also non-
linear Therefore it is not easy to solve these equations
without some approximations and simplifications of
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 49
Various difficulties in metal forming In many metal forming problems the boundary
stresses are unknown
As the plastic deformation proceeds the materialproperties go on changing due to strain hardening
At high rate of plastic deformation the temperature
o e e orm ng o y ncreases apprec a y w calso change the material properties
Phase change may take place during plasticdeformation which can also change the strength of
the metal body The nature of interfacial friction between tool and
metal is seldom known exactly
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 59
Different methods for solution Slab method
Slip line method Upper Bound method
Lower Bound method
Numerical techniques and Finite Element Method
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 69
Slab Method Plain sections remain plane during compression
Any non-uniformity in deformation is neglected Material is rigid perfectly plastic
Effects of strain hardening and strain rate are
neglected Method will be discussed later in details
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 79
983124983144983141983151983154983161 983151983142 983123983148983145983152 983116983145983150983141
Lines of maximum shear stress called slip lines
Slip lines are directions of maximum shear stressin the body undergoing plastic deformation
For plane strain deformation equilibrium equations
and yield condition (von Mises or Tresca) arerequired
Partial differential equations along with yield
condition in plain strain are hyperbolic partialdifferential equations
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 89
983096
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 99
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 39
The stress-strain relations in plasticity are non-linear
Yield condition in case of Von-Misesrsquo is also non-
linear Therefore it is not easy to solve these equations
without some approximations and simplifications of
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 49
Various difficulties in metal forming In many metal forming problems the boundary
stresses are unknown
As the plastic deformation proceeds the materialproperties go on changing due to strain hardening
At high rate of plastic deformation the temperature
o e e orm ng o y ncreases apprec a y w calso change the material properties
Phase change may take place during plasticdeformation which can also change the strength of
the metal body The nature of interfacial friction between tool and
metal is seldom known exactly
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 59
Different methods for solution Slab method
Slip line method Upper Bound method
Lower Bound method
Numerical techniques and Finite Element Method
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 69
Slab Method Plain sections remain plane during compression
Any non-uniformity in deformation is neglected Material is rigid perfectly plastic
Effects of strain hardening and strain rate are
neglected Method will be discussed later in details
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 79
983124983144983141983151983154983161 983151983142 983123983148983145983152 983116983145983150983141
Lines of maximum shear stress called slip lines
Slip lines are directions of maximum shear stressin the body undergoing plastic deformation
For plane strain deformation equilibrium equations
and yield condition (von Mises or Tresca) arerequired
Partial differential equations along with yield
condition in plain strain are hyperbolic partialdifferential equations
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 89
983096
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 99
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 49
Various difficulties in metal forming In many metal forming problems the boundary
stresses are unknown
As the plastic deformation proceeds the materialproperties go on changing due to strain hardening
At high rate of plastic deformation the temperature
o e e orm ng o y ncreases apprec a y w calso change the material properties
Phase change may take place during plasticdeformation which can also change the strength of
the metal body The nature of interfacial friction between tool and
metal is seldom known exactly
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 59
Different methods for solution Slab method
Slip line method Upper Bound method
Lower Bound method
Numerical techniques and Finite Element Method
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 69
Slab Method Plain sections remain plane during compression
Any non-uniformity in deformation is neglected Material is rigid perfectly plastic
Effects of strain hardening and strain rate are
neglected Method will be discussed later in details
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 79
983124983144983141983151983154983161 983151983142 983123983148983145983152 983116983145983150983141
Lines of maximum shear stress called slip lines
Slip lines are directions of maximum shear stressin the body undergoing plastic deformation
For plane strain deformation equilibrium equations
and yield condition (von Mises or Tresca) arerequired
Partial differential equations along with yield
condition in plain strain are hyperbolic partialdifferential equations
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 89
983096
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 99
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 59
Different methods for solution Slab method
Slip line method Upper Bound method
Lower Bound method
Numerical techniques and Finite Element Method
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 69
Slab Method Plain sections remain plane during compression
Any non-uniformity in deformation is neglected Material is rigid perfectly plastic
Effects of strain hardening and strain rate are
neglected Method will be discussed later in details
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 79
983124983144983141983151983154983161 983151983142 983123983148983145983152 983116983145983150983141
Lines of maximum shear stress called slip lines
Slip lines are directions of maximum shear stressin the body undergoing plastic deformation
For plane strain deformation equilibrium equations
and yield condition (von Mises or Tresca) arerequired
Partial differential equations along with yield
condition in plain strain are hyperbolic partialdifferential equations
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 89
983096
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 99
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 69
Slab Method Plain sections remain plane during compression
Any non-uniformity in deformation is neglected Material is rigid perfectly plastic
Effects of strain hardening and strain rate are
neglected Method will be discussed later in details
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 79
983124983144983141983151983154983161 983151983142 983123983148983145983152 983116983145983150983141
Lines of maximum shear stress called slip lines
Slip lines are directions of maximum shear stressin the body undergoing plastic deformation
For plane strain deformation equilibrium equations
and yield condition (von Mises or Tresca) arerequired
Partial differential equations along with yield
condition in plain strain are hyperbolic partialdifferential equations
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 89
983096
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 99
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 79
983124983144983141983151983154983161 983151983142 983123983148983145983152 983116983145983150983141
Lines of maximum shear stress called slip lines
Slip lines are directions of maximum shear stressin the body undergoing plastic deformation
For plane strain deformation equilibrium equations
and yield condition (von Mises or Tresca) arerequired
Partial differential equations along with yield
condition in plain strain are hyperbolic partialdifferential equations
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 89
983096
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 99
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 89
983096
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 99
7212019 MFM Lect 7
httpslidepdfcomreaderfullmfm-lect-7 99
