Title page for ETD etd-04262001-170912


Type of Document Dissertation
Author Jaber, Naim A
Author's Email Address njaber@vt.edu
URN etd-04262001-170912
Title Finite Element Analysis of Thermoviscoplastic Deformations of an Impact-Loaded Prenotched Plate
Degree PhD
Department Engineering Science and Mechanics
Advisory Committee
Advisor Name Title
Batra, Romesh C. Committee Chair
Hyer, Michael W. Committee Member
Klaus, Martin Committee Member
Nayfeh, Ali H. Committee Member
Ragab, Saad A. Committee Member
Keywords
  • Impact Loading
  • Failure Mode Transition
  • Finite Element Analysis
  • Thermoviscoplastic Deformations
Date of Defense 2000-12-13
Availability unrestricted
Abstract

Four different thermoviscoplastic relations, namely, the Litonski-Batra, the

Johnson-Cook, the Bodner-Partom and the power law are used to model the

thermoviscoplastic response of a material. Each one of these relations

accounts for strain hardening, strain-rate hardening and thermal softening of

the material. The material parameters in these relations are found by solving

an initial-boundary-value problem corresponding to simple shearing

deformations so that the computed effective stress vs. the effective plastic

strain curves match closely with the experimental data of Marchand and Duffy

who tested thin-walled HY-100 steel tubes in torsion.

These four viscoplastic relations are used to analyze dynamic thermomechanical

deformations of a prenotched plate impacted on the notched side by a

cylindrical projectile made of the same material as the plate. The impact

loading on the contact surface is simulated by prescribing the time history of

the normal component of velocity and null tangential tractions. A plane strain

state of deformation is assumed to prevail in the plate and its deformations

are studied for different values of the impact speed. The in-house developed

finite element code employs constant strain triangular elements, one point

integration rule, and a lumped mass matrix. The Lagrangian description of

motion is used to describe deformations of the plate. The coupled nonlinear

partial differential equations are first reduced to coupled nonlinear ordinary

differential equations (ODEs) by using the Galerkin approximation. The ODEs

are integrated by using the stiff solver, LSODE, which adaptively adjusts the

time step size and computes the solution within the prescribed accuracy.

Results computed with the four constitutive relations are found to be

qualitatively similar to each other and the general trends agree with the

experimental observations in the sense that at low speed of impact, a brittle

failure ensues at a point on the upper surface of the notch tip. However, at

high impact speeds, a ductile failure in the form of a shear band initiates

first from a point on the lower surface of the notch tip. The predicted speed

at which the failure mode transitions from brittle to ductile is different for

the four viscoplastic relations.

Results have been computed using the Bodner-Partom law to study the effects of

the notch tip radius and the presence of a circular hole ahead of the

notch-tip. For sharp elliptic notch tips, it is found that there is no failure

transition speed and the ductile failure always preceeded the brittle failure

for the range of the impact speeds studied. For the hole located on the axis

of the circular notch tip, the brittle failure always preceeded the ductile

failure and it initiated at a point on the lower surface of the circular hole.

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