4.5 DIC results on CFRP specimens
4.5.3 Off-axis tension of CFRP
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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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.
4.5. DIC RESULTS ON CFRP SPECIMENS
sub-linear trend.
When the angle θ is not zero (where a negative value will have the same effects of a positive value due to the obvious symmetric behavior), the behavior of the material is quite different.
First of all as the long warp yarns are not anymore parallel to the side edges of the specimen. It means that the warp starting from the lower tab may end to the right or left side of the specimen before reaching to the upper tab. This important geometric characteristic cause high strains inside the material even if just tensile loads are applied. In fact the effect of yarns that cannot completely bear the load tends to make them rotating and shearing one over the other. This effects lead to a more complex strain distribution and a much weaker response of the material, that needs to be investigated. For this purpose specimens with three different angles θ were cut and tested. The three angles are 0◦, 30◦ and 45◦ respect to the loading direction. The experimental set-up is the same in all test configurations, as depicted in Figure 4.16.
(a) 0◦specimen (b) 30◦specimen (c) 45◦specimen
Figure 4.29: Field of view of the three specimen configurations for off-axis tensile tests
The DIC set-up is mainly the same in all tests, except that for the specimens of 30◦ the field of view is smaller respect to the other two configurations. In order to reduce the effects of small aperiodicity of the material the bigger area provided by 0◦ and 45◦ configurations are more preferable as these two configurations present a bigger field of view (see Figures 4.29(a) and 4.29(c)). For 30◦the area of interest is smaller. Therefore it is possible to have more localized strain information (see Figure 4.29(b)).
A first result can be a macroscopic information on the strain evolution of the specimen, done by averaging the strain data over the area of interest. This can be an important result as it can give useful information about the effect of off-axis loading of CFRP laminates, especially the elastic modulus along the loading direction. An observation of the specimen surface followed by DIC strain analysis and synchronization of these data with stress information coming from tensile testing machine lead to the graph of Figure 4.30.
It is obvious that the stress-strain curve of the specimen with 0◦ configuration is almost a straight line (or sub-linear). This has been discussed in Section 4.5.2.
The specimen with 45◦ configuration has a similar field of view and therefore it has similar strain distribution. However the stress-strain curve is different from the 0◦configuration. All the warp yarns starting from one tab cannot reach to the other tab. Because the distance between the tabs is 180 mm and the width of the specimen is 25 mm and this means that the minimum
4.5. DIC RESULTS ON CFRP SPECIMENS
(a) 0◦specimen
(b) 30◦specimen
(c) 45◦specimen
Figure 4.30: Stress-strain curves of tensile tests on three different oriented specimens
angle to have a complete disjointing is about 8◦. Moreover in central areas, enough far from the borders, the 45◦ configuration under tension leads to a localized pure shear loading condition.
In fact the shear stresses and strains are preponderant. The behavior of the material is mainly due to the mechanical properties of the polymeric matrix and the elongation before final failure is very high. Actually in some cases it is even difficult to define a final failure, as after several centimeters of displacement of the crossheads the material looks non damaged (but it has lost its strength and it is highly damaged).
As shown in Figure 4.30(c), at mean strain value of about 2% the strength of the specimen has reached to the value of 100÷110 MPa with a clear non-linear behavior. After this value the material is mainly damaged and just the matrix plus the pullout resistances5are bearing the load applied to the specimen. A sub-linear stress-strain curve with a slope of 1455 MPa is continuing till 160 MPa and a strain of 6.3% which is the final failure point.
The specimen with 30◦configuration was observed by a higher magnification to reveal better the intra-yarns heterogeneities. The field of view has a size of about 9x6.7 mm2. Thus each pixel has a size of 6.45 µm. Such magnification leads to a smaller observable elongation by the digital camera that is obviously fixed during the test. Therefore the achieved results last till an average
5Pullout effect is mainly related to the friction between yarns and the ability of the fabric to absorb energy. This is especially important in ballistic applications [69]
4.5. DIC RESULTS ON CFRP SPECIMENS
strain of 3% (see Figure 4.30(b)). The same as the previous specimen (45◦ configuration), the warp yarns starting from a tab cannot reach the other tab. Here the elongation before final failure is again very high and the maximum force is considerably lower than the case of 0◦. The strength of the material is slightly higher then the specimen with 45◦ configuration. However it is still quite lower than the specimen with 0◦ configuration.
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Figure 4.31: Elastic modulus vs. off-axis angle curve
Figure 4.31 shows the trend of the elastic modulus respect to the off-axis angle and the important effects of the off-axis angle on mechanical behavior of the composite material. Even for few degrees the elastic modulus is quite lower for example in 20◦ configuration the elastic modulus is almost half of 0◦configuration. This macroscopic result is very important during the designing process as it gives useful information about the tolerances on geometrical characteristics of the component to the designer.
Skipping the results of 0◦configuration because it has already been discussed in Section 4.5.2, hereafter some considerations about the strain maps of the other two configurations will be discussed. In particular the capabilities of DIC method will be considered.
In Figure 4.32 the strain map evolution of the specimen with an off-axis angle of 45◦is shown.
The graph in the middle shows the stress-strain curve from the beginning of the experiment up to the time that the area analyzed by DIC moves outside the camera view. Here again four time