Nonlinear Load-displacement Behavior Research Articles

The effects of specimen size and testing conditions on fracture toughness evaluation of polypropylene homopolymer

AbstractThe results of an experimental test program performed to investigate the influence of specimen dimensions and testing rate conditions on room temperature fracture toughness of PP homopolymer are presented. The material displayed nonlinear load‐displacement behavior and exhibited small amounts of slow crack growth (ductile tearing) prior to cleavage instability, which invalidates the direct application of the current standards for the determination of KIC in polymers. Data points were considerably scattered consistently with typical ductile‐brittle transition patterns. The resulting load‐displacement diagrams were analyzed in terms of KQ, KMAX, and the ratio PMAX/PQ. THe fracture toughness at instability, JC, was also computed and plotted against the amount of stable crack growth in order to construct J‐R curves as a function of size and strain rate. From these curves an alternative critical fracture parameter, KJIC, was calculated. Weibull statistics were used as a tentative approach for treating the scatter of fracture toughness of polypropylene homopolymer in large samples, which exhibited restricted ductile tearing. The significance of each of these methods and the validity and size independence of the corresponding parameters are discussed.

In vitro evaluation of shoulder external rotation after a Bankart reconstruction.

The Bankart procedure is a commonly performed anterior shoulder reconstruction that may shorten the anterior capsule. In this study, biomechanical testing was performed to evaluate the effect of the classic Bankart reconstruction on external rotation of the shoulder. The procedure was performed on six fresh-frozen cadaveric specimens that were free of intraarticular pathologic changes. With the arm in 0 degrees of abduction, resisting torques about the vertical axis were measured while the humerus was externally rotated. The intact specimens demonstrated a nonlinear load displacement behavior in which little resisting torque was measured until a moderate amount of external rotation was applied. Shortening the capsule by 2 mm resulted in a 40% decrease in the low-tension zone of external rotation, and shortening the capsule an additional 5 mm resulted in a 67% decrease in the low-tension zone. This study demonstrates that the normal shoulder capsule is quite sensitive to anterior capsular shortening and suggests that care must be exercised when performing a Bankart reconstruction to avoid overtightening this structure.

On the Uncertainties Involved in Quantifying the Fracture Toughness of Al-Li-X Alloys

Abstract The fracture behavior of an extruded Al-2.6Li-0.09Zr alloy in a near peak-aged and over-aged condition was found to be primarily intergranular with formation of non-Mode I, crack-divider delaminations at the crack tip especially in the over-aged temper. This complex, irregular fracture mode results in behavior that cannot be accurately measured using the conventional J- and K-based toughness parameters and testing methods. Other observed fracture characteristics that force reassessment of the traditional testing methodologies include crack length variations, mixed mode fracture from crack deflection, and apparent plasticity. The observed crack length variations through the specimen thickness led to 4 to 8% uncertainty in the K-curve for the specimens used. Furthermore, crack deflection corrections lead to an average 4 to 7% and maximum 15 to 18% apparent toughness increase for the material. The alloy exhibited nonlinear load-displacement behavior during fracture that could be corrected by using a plastic zone size modification. The analyses outlined provide insight into the roles the various mechanisms play in the fracture process of this alloy. However, the conventional toughness measures were inadequate in treating the observed fracture behavior.

A formulation and solution procedure for post-buckling of thin-walled structures

Transformations of nodal quantities between spacially fixed global coordinate system and element fixed local one are presented to give governing equilibrium equations for a post-buckling large displacement analysis of thin-walled three-dimensional structures. The transformations are established primarily on the basis of the description of the nodal locations by their initial coordinates as well as their displacements. An effective corrective process for constituting and solving structural incremental nonlinear equilibrium equations is developed by clear separation of the rigid body rotation from the displacements. Numerical examples show that the method can satisfactorily pursue nonlinear load-displacement behaviour, including snap-through and bifurcation buckling, only with incremental calculations and without any special techniques as eigenmode analysis.