J-Integral Calculation by Finite Element Processing of Measured Full-Field Surface Displacements

Abstract

A novel method has been developed based on the conjoint use of digital image correlation to measure full field displacements and finite element simulations to extract the strain energy release rate of surface cracks. In this approach, a finite element model with imported full-field displacements measured by DIC is solved and the J-integral is calculated, without knowledge of the specimen geometry and applied loads. This can be done even in a specimen that develops crack tip plasticity, if the elastic and yield behaviour of the material are known. The application of the method is demonstrated in an analysis of a fatigue crack, introduced to an aluminium alloy compact tension specimen (Al 2024, T351 heat condition).

Procedure for accurate calculation of the J‐integral from digital volume correlation displacement data

“… σ ij is calculated using Equations and . In this work, Equation is given under the assumptions of a linear‐elastic isotropic material; however, more complex mechanical behaviour models may be used such as presented by Barhli et al …”

“…Each segment has a width of ΔS . In this work, the crack‐tip location and direction are segmented visually; however, other methods are available …”

“…State‐of‐the‐art subset‐based correlation techniques suffer from smearing of information across the crack faces resulting in spurious displacement and strain readings. It is therefore imperative for DIC‐ and DVC‐based fracture property extraction methods to account for these sources of error by (a) using significantly more complex (and generally in‐house developed) correlation techniques (e.g., subset splitting); (b) replacing poorly defined or missing data in these regions (e.g., with numerical approximations of the material after the crack front has been found); or (c) developing methods that allow for the selection of data remote from the crack tip thereby eliminating the need for accurate displacement data near the crack faces and crack front …”

“…The poorly defined displacement fields, in combination with the need for accurate displacement data around the crack front, create a need for a unique implementation of the J ‐integral. One method to overcome this is to replace the missing, or censored, data using the finite element (FE) framework, as presented by Bahrli et al However, this requires extrapolation from the measured data in order to define a displacement field in the cracked region, which in turn requires assumptions on the material properties (plasticity and microcracking) in this region, and the method cannot consider the effects of complex fracture mechanics such as crack branching or bridging. This extrapolation also requires knowledge of the precise crack front location.…”

Fatigue crack closure: A myth or a misconception?

“…The results show consistent stress‐strain responses around the crack tip in the distances of interest for COD and strain measurements. Data in a region close to the crack wakes (Figure A) were excluded to reduce the noise because of noncorrelation errors in the DIC anaylsis . Similarly, DVC data within a quarter circular volume with a cross‐section of 2.7 × 0.4 mm around the 3D crack flanks were also excluded (Figure B) for the same reason.…”