JMAN : J-integral calculation

The J-integral is a way to calculate the energy released propagating a crack per unit area. The value of calculated J-integral is theoretically independent from the chosen contour, provided that the material is elastic.

We will see how in JMAN we calculate the J-integral value from a displacement field.

The input data are the results of digital image correlation analysis or the results of a finite elements calculation. The input requires the 2D coordinates of the points at which measurements (or calculations) were performed along with the respective 2D displacement values.

The first step is to create a finite element mesh were the input values are the values at the nodes of our mesh.

Fig 1. Mesh of quadratic elements

Once this mesh is created, we will calculate the stress and strain values at the integration points. From those results, a contributive term for J at each element in the chosen contour is determined.

Fig 2. Example of a J-integral contour

The final step is to retrieve the J-integral value by summing the J contributive terms of each element in the contour.
The value of K, the stress intensity factor is easily determined from the value of J.

JMAN : introduction

I decided to start a series of posts about a software we are developing using Matlab. This program, called JMAN (J-integral calculation method developed in MANchester), allows the user to determine the stress intensity factor from images taken from surface of a specimen. A first version of JMAN was already implemented, see here.

The user starts performing a fracture test experiment and take pictures of the crack zone at different moments of the experiment, then he runs a Digital Image Correlation analysis in order to get the displacement field.

JMAN takes as input the material properties (Young modulus, Poisson ration) and results of the Digital Image Correlation.

In a first time we will talk about how the program works and present some examples based on Abaqus models. Then we will see how the experiments parameters (DIC parameters, camera parameters...) influence the results. Finally we will talk about the limitations of JMAN.

GPU calculation : final step

We can see on the graphs that GPU calculation provides an acceleration only for large data sizes.

This is due to the fact that for small data sizes, the time spent transferring data to the GPU is higher than the time gained during calculation.

Here the speed-up factor is not high enough for us to use GPU calculation instead of CPU calculation.