Stress Vs Strain using DIC

Standards

Sample Dimensions

Choosing Pattern Quality

Pattern 3 & 4:

Choosing two different types of pattern sizes, Pattern 3 & Pattern 4, leaves us with two options. Pattern 3 has smaller ROIs and a larger area to cover minor changes along the image. It has a minor defect in the pattern due to a larger black dot in the image, but this is not close to the area with the highest strain. On the other hand, Pattern 4 has larger ROIs and completely covers the affected area. The issue arises regarding whether to choose a better pattern with a smaller area or a larger area with a minor defect located away from the area with the larger strain.

The final pattern, Pattern 3, was chosen for the purpose of examining minor changes along the image.

As we analyze the pattern quality, we observe that pattern quality plays a major role in analyzing the data at various stages of the test. Analysis with smaller DOIs tends to pick up more details that can be further helpful, such as localizing different regions of strain that cannot be seen with larger DOIs.

Upper and Lower Bounds of the Engineering Stress-Strain Curve

The upper and lower bounds of the engineering stress-strain curve, can be calculated with:

From the uncertainty estimations above, we know that the total error of the engineering stress is 1.43%, so the upper and lower bound becomes:

And can be expressed graphically as:

Fit for the Elastic Modulus

First, we selected the initial and farthest points in the elastic region by identifying both regions on the stress-strain curve

After this, we made a linear approximation from the start of the plot to the point selected before, using the equation described on

Standard E111-17 [1], section 9.3.2:

And we found the intersection with the Stress axis with MATLAB’s Curve Fitting Tool to be -27.52.

The fitting for the Elastic Modulus becomes:

Comparison with Results of Lab 1 (Tensile Test)

Even though both results remain similar through most of the test, they separate their ways when the samples are about to go through fracture. This might be caused by how localized the strain calculation is when using DIC. We should consider that when looking at the behavior of the sample using only the machine, an average strain is obtained. The difference between both procedures could be explained to be similar to the difference between a coarse and a fine mesh when analyzing a mechanical behavior through FEM.

True vs. Engineering Stress-Strain Curve

Since the true stress considers the decrease of the area as a function of time, the stress value keeps increasing, even after reaching the ultimate stress. While on the engineering stress-strain behavior, the area remains constant. Therefore, the stress value decreases after reaching the ultimate stress (necking allows a high strain with lower tension forces).

Poisson’s Ratio

Poisson’s Ratio – Elastic Region

Poisson’s Ratio – Plastic Region

Evolution of Tensile Strain Along the Long Axis

Strain tends to be higher in the area where fracture is most likely to occur. In the beginning stages where necking is about to initiate, higher strain regions could be observed along the specimen. Changing for a finer pattern quality as seen in the picture below there are areas of strain in which higher singularities of strain can be observed.

One of the possible reasons for this observation could be due to nano ridges/fractures/holes along the material itself. As it is being stretched in a specific direction the realignment of the grains of aluminum might cause these regions to appear in the analysis, or smaller holes can also play a part in the specimen’s integrity. As necking/strain increases the observation of these singularities is less frequent and the accumulation of strain is concentrated in a specific length of the specimen.

As necking is started to be perceived in the specimen, the strain value increases significantly until its fracture .[0.200-0.356] is the arrange of strain that we observe in this region.

As we further analyze the strain propagation in the necking are we observe that the maximum strain occurs close to the center of the specimen thus visually estimating that a crack might have occurred in the center and propagated outwards causing the fracture of the specimen in an angle .

Elastic Recovery

Elastic recovery is the part of the sample that does not neck , but experiences a reduction of strain after fracture. We will use two images from the test to determine the elastic recovery. One at the maximum strain before fracture and the other the strain directly after the fracture has occur. GOM correlate is able to measure both strains and directly plot strain vs time of these two events.

The Strain decreases from a maximum of 0.12969 to 0.12591, giving us a strain recovery of 0.00378.