SS-V: 5080 Rigid Punch Plasticity

Test No. VNL09 Find out reactions at the punch pressed on large block for perfectly plastic and isotropic hardening materials.

Definition

A 2D plane strain punch is pressed on larger block of finite dimensions. Punch is assumed rigid and contact condition between punch and the block are assumed frictionless sliding (line BC). Vertical downward displacement D is applied to the punch (Figure 1). Symmetry condition is assumed along line ABL, and sliding condition is applied along line LK.


Figure 1.

Dimensions: AB = 40 mm, BC = 80 mm, BL = 160 mm, LK = 200 mm

The material properties are:
Properties
Value
Modulus of Elasticity
1.e+3 MPa
Poisson's Ratio
0.3
Two plasticity models are used:
  • Elastic perfectly plastic with yield stress 1 MPa
  • Isotropic hardening with tangent modulus 0.1e+3 MPa

Results

Geometry of rigid punch and the base was simulated with two 3D solid plates with thickness 10 mm (Figure 2a). Plane strain condition assumes zero strain perpendicular to the plate side. In order to meet the condition zero normal displacements were applied to both sides of the plates (Figure 2b).


Figure 2.
Prescribed displacement of the punch was applied in six steps. The following table contains values of the reaction force at the punch per 1 mm of the plates thickness.
SimSolid Reaction, N Reference Reaction, N
D, mm Perfect Plasticity Hardening Perfect Plasticity Hardening
0.04 29.57 29.57 30 30
0.12 86.95 87.27 86 87
0.14 99.93 100.65 99 100
0.16 108.22 111.17 109 113
0.18 108.87 113.03 110 114
0.24 111.75 122.20 111 125
The figures below show evolution of equivalent stress with the punch displacement increments.


Figure 3. Left: Perfectly Plastic Material; Right: Isotropic Hardening Material. D = 0.04 mm


Figure 4. Left: Perfectly Plastic Material; Right: Isotropic Hardening Material. D = 0.12 mm


Figure 5. Left: Perfectly Plastic Material; Right: Isotropic Hardening Material. D = 0.14 mm


Figure 6. Left: Perfectly Plastic Material; Right: Isotropic Hardening Material. D = 0.16 mm


Figure 7. Left: Perfectly Plastic Material; Right: Isotropic Hardening Material. D = 0.18 mm


Figure 8. Left: Perfectly Plastic Material; Right: Isotropic Hardening Material. D = 0.24 mm
1 Test PL-7 from NAFEMS Publication R0049, “Background to Material Non-Linear Benchmarks”.