Date of Award

Summer 1986

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical & Aerospace Engineering


Engineering Mechanics

Committee Director

S. G. Capschalk

Committee Member

J. C. Newman

Committee Member

C. Mei

Committee Member

Zia Razzaq

Committee Member

K. N. Shivakumar


The purpose of this study was to develop a three-dimensional, elastic-plastic, finite element analysis to investigate crack extension and closure under cyclic loading. The initial study concentrated on the behavior of a straight through crack in a finite-thickness plate subjected to tensile loading (middle-crack tension specimen). The finite element model was composed of 8-noded (linear-strain) isoparametric elements. In the analysis, the material was assumed to be elastic-perfectly plastic. Zienkiewicz's "initial-stress" method, von Mises' yield criterion, and Drucker's normality condition, under small-strain assumptions, were used to account for plasticity. The three-dimensional analysis is capable of extending the crack and changing boundary conditions under cyclic loading. Initially, the crack was assumed to grow as a straight-through crack.

The analysis was applied to determine crack-opening and closure stresses for a middle-crack specimen used in an ASTM Committee E24 task group activity on crack closure. First, imposing proper boundary conditions on the three-dimensional model, plane-strain conditions were simulated and then the model was subjected to a cyclic stress level of 0.25 σys, where σys is the yield stress of the material. Next, a complete three-dimensional analysis of the specimen was made at stress levels of 0.2 σys. and 0.25 σys. . For the highest stress level considered, the ratio of crack-opening stress to maximum applied stress for the outer and inner regions of the model were found to be 0.56 and 0.34, respectively.

The crack-surface displacements for the outer and inner regions of the model, and the variations of normal stresses in the x and y direction are plotted as functions of coordinate location for the stress level of 0.25 σys. The behavior of normal stress in the z direction, through the specimen thickness, for specified elements along the crack plane was also presented. In all of these results, the three-dimensional constraint effect caused higher crack-surface displacements and higher normal stresses on the inner region of the model than those for the outer region. Crack-opening stresses were also determined using displacements at specified points along the crack plane using a load-reduced-displacement technique.