Numerical study of constraint effects on dynamic ductile crack initiation

Abstract

Dynamic Loading Effects on Fracture Toughness and Crack Tip Constraint in Engineering Alloys

Abstract and Synopsis Introduction In many engineering applications, materials are subjected to highly dynamic loading. Experimental evidence shows that engineering alloys generally exhibit higher fracture toughness under dynamic loading, particularly when failure occurs by ductile void coalescence. Numerical investigations further suggest that fracture specimens display large negative T-stress during the early stages of dynamic loading compared to static cases. In elastic-plastic solids, this results in a significant loss of crack tip constraint (stress triaxiality).

The objective of this thesis is to systematically study constraint loss in three-point bend (TPB) specimens subjected to dynamic loading and to investigate whether this phenomenon is responsible for the observed enhancement in fracture toughness.

Boundary Layer Simulations

Conducted by imposing different T-stress levels or biaxiality ratios.

Studied the interaction between a notch and a void ahead of it using the Gurson constitutive model.

Results: Negative T-stress retards void growth and porosity development in the ligament between notch and void.

The critical J-integral value for ligament failure (Jc) increases strongly with negative T-stress (constraint parameter Q).

TPB Specimen Analysis

TPB specimens with varying notch length-to-width ratios (a/W) analyzed under static and dynamic loading using 2-D plane strain finite element methods.

Employed finite deformation version of the J-flow theory of plasticity.

Results: A valid J-Q field exists under dynamic loading regardless of a/W ratio.

Constraint parameter Q becomes more negative with increasing loading rate, especially for a/W > 0.5.

Ductile Fracture Processes under Dynamic Loading

Studied microvoid nucleation, growth, and coalescence in TPB specimens at different loading rates.

Results: Loading rate effects mimic those caused by negative T-stress.

Predicted fracture toughness increases strongly at high J values, consistent with experimental observations.

A simple model combining the Jc-Q locus (from boundary layer analyses) and J-Q trajectories confirmed that inertia-driven constraint loss causes toughness enhancement.

Conclusions Dynamic loading induces negative T-stress, leading to loss of crack tip constraint.

This constraint loss retards void growth, increases Jc, and enhances fracture toughness.

The effect is more pronounced at higher loading rates and larger notch ratios (a/W > 0.5).

The study confirms that inertia-driven constraint loss is the mechanism behind enhanced fracture toughness under dynamic loading.