4.5 DIC results on CFRP specimens
4.5.2 DIC vs. FEM
After a first and rough validation of the method, a more important comparison was performed:
a comparison between the DIC strain fields and the strains calculated by finite element models of CFRP laminas. This comparison has a twofold meaning: validate DIC using low strains data obtained by FE model and set the material parameters of the FE model using high strains data (non-linear behavior).
This two-way setting is possible because DIC is able only to evaluate the strains. Then considering that at the linear regime, according to an average strain value in the unit-cell, the strain field on the whole cell is not strongly dependent on the mechanical parameters of the materials used to build the model. Thus the FEM can be used to compare the strain results with DIC data. When the stresses are used, the approach is different and so that mechanical properties are much more important as in this case there are different stresses for the equal strains. Moreover the damage criteria implemented in the numerical model are mainly working at high strains and so the non-linear behavior of the material is emphasized.
The tests were performed mainly with two different lenses. One at the magnitude of 0.75X with the lens TVML/Z4.5 and so a field of view of about 13x9.8 mm2 that is 2.2 times bigger than the area of the unit-cell (that is about 7.7x7.7 mm2). The dimension of each pixel is about 9.45 µm. The second one with the lens GMZ135108 and with a field of view of about 48.3x36.1 mm2that is 29.4 times bigger than the area of the unit-cell. The dimension of each pixel is about 34.7µm. As the warp yarns are along the loading direction and the weft are perpendicular to it, the axis y will be referred as “longitudinal” direction (the direction of loading) and the axis x as
“transverse” direction. Thus the �y refers to a longitudinal strain, �xrefers to a transverse strain and γxy refers to shear on the plane xy.
Some strain maps will be analyzed and discussed in the following pages. The maps are usually presented with the x − y coordinates in pixels. Moreover the dimension of the studied area depends on several afore discussed considerations, and so will not be directly related to the dimensions of the images presented here.
Strain components
An important aspect of the DIC method is that it is easily able to calculate all the components of the strain tensor on the surface of the specimen. This means that it gives directly the two normal strains �x and �y as well as the shear strain γxy. Whereas DIC has an almost constant precision over the displacement and not proportional to the absolute values, lower values have higher errors. An example is shear strain which is usually at least one order of magnitude less than the longitudinal mean strain.
4.5. DIC RESULTS ON CFRP SPECIMENS
(a) �x
(b) �y
(c) γxy
Figure 4.19: Strain maps of a CFRP specimen under tension, at an average longitudianl strain of 0.15%
Figure 4.19 shows the strain maps related to a specimen under tensile loading with an average strain along the loading direction of 0.15%. It is possible to see that in the areas of positive longitudinal strains, there are negative transverse strains, due to the Poisson effect. It is also obvious that the complex architecture of the material leads to a complex distribution of the Poisson’s ratio. Despite of what expected the longitudinal strain distribution has negative values that can be probably due to numerical approximations, errors of the DIC calculations or local defects on the images. On the other hand the shear distribution is almost symmetric and with low values (as it is expected from this kind of test). The problem aforementioned is also due to the low measured values (the average longitudinal strain is just 0.15%). In fact considering higher average strain condition would give better results.
(a) �x
(b) �y
(c) γxy
Figure 4.20: Strain maps of a CFRP specimen under tension, at an average longitudianl strain of 1.12%
Figure 4.20 shows a situation where the average longitudinal strain is 1.12% (close to the final failure). In this situation the longitudinal strain is never negative as it is expected.
4.5. DIC RESULTS ON CFRP SPECIMENS
Strain evolution
Another important information achieved by DIC method is the capability of obtaining the complete strain evolution of the specimen surface during the entire test4, for each component of the strain tensor. Figure 4.21 shows the strain evolution of the longitudinal strain �y. Four different time instants are selected and plotted, starting from early stages till the final failure.
Each map has been selected with an average strain about 0.3% higher than the previous map.
Figure 4.21: Strain evolution of a CFRP specimen under tension, from early stages till final failure
In order to reveal better the differences and the localization of strains the color range is selected equal in all the maps. It is clear that the same process can be exerted for all the components of the strain tensor. At the same way it is possible to select one point of the
4This statement is true till the defined analysis grid is not moving outside the observed area.
4.5. DIC RESULTS ON CFRP SPECIMENS
analyzed grid, or average the values of an area and follow its evolution.
Figure 4.22: Longitudinal strain evolution of a CFRP specimen under tension with comparison between minimum values, maximum values and mean values
Figure 4.22 shows the evolution of the longitudinal mean strain during the test in a 0◦oriented specimen (continuos line). The two dashed lines are representing the curves of minimum and maximum strains of each frame during the test on all the analyzed area.
(a) Transverse strain evolution of the entire analyzed area
(b) Transverse displacement evolution of one point
Figure 4.23: Exmaples of strain and displacement evolution along the transverse direction
More complex strain evolution curves can be found using the other two components of the strain tensor. In Figure 4.23(a) the curves representing the minimum, maximum and mean transverse strains are presented. Figure 4.23(b) represents the evolution along the time of the displacement of a single point of the analyzed grid. This curve well represents the complex
4.5. DIC RESULTS ON CFRP SPECIMENS
plane movements.
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Figure 4.24: Longitudinal strain evolution of a CFRP specimen under tension. Data along x axis, at the middle of the specimen
Another interesting output of DIC method is shown in Figure 4.24. The figure shows four plots of longitudinal strain �y measured along the axis x, at a y coordinate almost at the middle of the specimen. Different plots, taken at different time instants during the test, show the evolution of the strain which is mainly keeping the shape, but increasing the values according to the increasing damage of the specimen.
Architecture superposition
The ability of the technique to observe the surface directly provides the direct superposition of the strain map over the material architecture or micro-structure. In fact as the method is defined by the observation of the surface of a specimen, it is easily possible to define all the moving sub-windows in the bi-dimensional space of the image, in pixel coordinates. This is very powerful as it allows the user to understand what is the cause of the presented behavior.
In Figure 4.25 the architecture reveals that the transverse yarns have higher deformations.
The reason of this behavior will be explained better later.
The approach encounters with some difficulties when the specimen needs to be painted as the paint hides the material structure. This is the case of CFRP specimens as described in Section 4.4.2. Furthermore if the painting technique is based just on the deposition of white dots, there is still one possibility. Considering the specimen already mounted in the testing machine and ready to start the test, an accurate selection of the illumination can reveal the material below the painting. This single image can be used to find the position of the yarns.
4.5. DIC RESULTS ON CFRP SPECIMENS
Figure 4.25: Architecture superposition on the strain maps of a CFRP specimen
Comparison with FEM results
Figure 4.26 shows a FE model of a twill weave 2x2 unit-cell made of CFRP where the matrix has been removed to make the yarns more visible. According to the model described in detail later (see Chapter 5) the model has been built and loaded to simulate a tensile test on a infinite media (made by a continuous repetition of unit-cells in x and y directions, which are both lying on the plane of the ply).
Figure 4.26: FE model of a twill weave 2x2 unit-cell made of CFRP
In order to compare just the strains, localized comparisons were performed using configura-tions where the average strain on the three-dimensional unit-cell of FE model equals the average strain on the bi-dimensional DIC grid (or as close as possible). Once the overall strain is the same, the local comparison assumes greater significance.
4.5. DIC RESULTS ON CFRP SPECIMENS
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Figure 4.27: DIC vs. FEM average strain data
for example shown also in Figure 4.22). In the same plot the homogenized value of longitudinal strain obtained from the finite element model has been added (it is important to notice that the frame index axis is meaningless for FE model). The x-axis position of the FE data reveals the DIC frame with closer strain values. The error between FE results and DIC results at the selected time instants (that cannot be exactly the same) are shown in the same graph.
Table 4.4: DIC – FEM matching FEM increment DIC frame Difference [%]
0 8 0.00%
1 23 0.59%
2 39 1.60%
3 55 0.35%
4 72 0.00%
5 90 0.00%
6 107 0.33%
7 125 0.11%
8 143 0.22%
9 159 0.20%
10 176 0.16%
The Table 4.4 shows matching between DIC frames and FEM increments coupled also with the percentage difference between the average strains. The values are quite good (the highest is just 1.6%) because of the high number of DIC frames (195 frames for 1.2% of final failure strain) and so the maximum error is due to a strain difference of half of the distance between
4.5. DIC RESULTS ON CFRP SPECIMENS
two consequent frames that is 12 · 1.2%195 ≈ 0.00308%. This leads to an error of roughly 1.6% as here obtained for the third value (FEM increment 2).
A comparison between FE and DIC results can be done by selecting some time instants and define a transverse line at a specified y coordinate and compare the results from FE model and from DIC calculations. According to the coordinate system of Figure 4.26 the x axis of the DIC images corresponds to the yF EM axis of the FE model. Moreover, according to how the model has been built and the specimen has been mounted on the testing machine, the observed surface is the one at negative values of zF EM.
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(a) ��y� = 0.32%
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(b) ��y� = 0.66%
Figure 4.28: DIC vs. FEM comparison of the values along the x axis
Figure 4.28 shows the comparison between DIC and FE at two different strain levels. As the field of view was enough big to observe all the specimen width and the analyzed area was just few millimeters smaller (to avoid border effects), DIC results are able to complete almost three different unit-cells and so it is possible to see three times the behavior of the single unit-cell that actually is shown by FE results (black line in the graph). The well matched results demonstrate the ability of the method to reveal local strains with high precision.