Damage Magnitudes

Damage magnitudes are identified using Maximum Stress Criteria (MAXSCRT) contours. MAXSCRT contour is a plot of the ratio of stress computed by the FEM model due to applied deformation over ultimate stress or strength measured in the laboratory as described in Eq. (4.3). Upon applied deformation and using Eq. (4.1), for each integration point of an element, the normal and shear stresses are calculated; the calculated normal and shear stresses are normalized by using Eq. (4.3) for two dimensional FEM model; the maximum normalized value between the two ratios are the critical normalized value and showed as MAXSCRT value in the contour diagram. MAXSCRT is a unit less value since it is a ratio of two stresses. The maximum value of MAXSCRT is 1.0. When MAXSCRT value is 1.0 for an element than that particular element is known as damaged element for the whole domain. When MAXSCRT value is less than 1.0 for an element, the element is not damaged yet but will or might damaged upon increase of load magnitude or increase of duration of load or decrease in material thickness. The two deformations are used to see the changes in damage initiation and progression due to increase of deformation magnitudes; three load patterns are used to see the changes in

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damage initiation and progression due to changes of duration of applied deformation; thin and thick matrix are used to see the change in damage magnitude due to change in thickness.

According to Table 4.1, the E-value for normal direction is higher for dry samples than wet samples, so, for same deformation and using Eq. (4.1), the normal stress under dry condition is higher than wet condition. On the other hand, the maximum normal stress is also significantly higher under dry condition than wet condition, so, the normalized value calculated using Eq. (4.2) for dry condition might lower than wet condition. If E-value for shear directions are considered, the dry sample has lower E-value than wet sample, so, for the same deformation or strain and using Eq. (4.1), the shear stress is lower under dry condition than wet condition. Furthermore, the maximum shear stress is significantly higher under dry condition than wet condition, so, the normalized value calculated using Eq. (4.2) for dry condition might lower than wet condition. While comparing the normalized normal and shear stresses under dry or wet condition, ABAQUS solver picks the highest value between two and shows as MAXSCRT value for that particular condition.

In addition to deformation value, the duration of applied deformation is also important for progression of damage. Maximum deformation is applied for a specified time step. For triangular pattern, deformation increases over time and the maximum deformation applied for almost zero second or instantaneously, for sawtooth pattern, maximum deformation applied for 0.04 sec and for rectangular pattern, maximum deformation applied for almost 0.0999998 sec. Damage inside the material is higher when deformation is applied for longer time. The reason behind, when damage initiates due to

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applied deformation in some elements (i.e. MAXSCRT value is 1.0), that element does not carry any stress for the rest of the analysis period. For this reason, stress carrying capacity increase for adjacent elements and their MAXSCRT value increases over time and damaged if normalized value exceeds 1.0 and the process continues until the end of analysis period. It is expected that rectangular pattern shows higher damage locations than sawtooth or triangular pattern since the applied deformation is applied for longer time period.

Moreover, thickness of matrix on aggregate might help prevent damage inside the matrix material. Thicker matrix provides higher stress carrying capacity since more area of matrix is taking stresses. Thick matrix will carry higher deformation and distribute stresses evenly into the larger area to reduce damage than thin matrix.

The maximum MAXSCRT values for the whole model of wet and dry samples are plotted in Figure 4.5 for three intensity patterns for 0.72 mm (0.0285 in.) and 1.45 mm (0.057 in.) applied deformation on thin and thick matrix. Maximum MAXSCRT values are taken from the contour plots. Comparing Figure 4.5(a) and 4.5(b), and Figure 4.5(c) and 5(d), it can be seen that MAXSCRT values for thick matrix is lower than thin matrix for triangular and sawtooth pattern. Rectangular pattern shows highest MAXSCRT value for both thin and thick matrix in all cases. Indeed, thicker matrix is less damaged than thinner matrix for both dry and wet conditions and proved that thicker matrix sustain more deformation than thinner matrix. On the other hand comparing Figure 4.5(a) and 4.5(c), and 5(b) and 5(d), it can be seen that maximum MAXSCRT value increases due to increase of applied deformation. Also wet samples show higher maximum MAXSCRT value than dry samples and prove that wet samples are more damage prone than dry

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samples. Reasons for showing higher MAXSCRT value under wet condition comparing to dry condition is explained in the following sections. Also maximum MAXSCRT value increases when load intensity pattern changes from triangular to sawtooth to rectangle. This supports the argument that, duration of applied deformation influences damage in the matrix and more damaged locations are exposed inside the matrix material.

In Figure 4.5 (a), the maximum MAXSCRT value is about 0.68 under dry conditions and 0.73 under the wet conditions for the triangle pattern. Since for the triangular loading, the MAXSCRT value is less than 1.0, so no element is damaged. The MAXSCRT value in some elements reaches the maximum value of 1.0 under both dry and wet conditions for sawtooth and rectangular patterns. So for both sawtooth and rectangular patterns there are damaged elements. According to Figure 4.5(b), the maximum MAXSCRT value is about 0.06 under the dry condition and 0.09 under the wet condition for triangular pattern; the maximum MAXSCRT value is about 0.11 under dry condition and 0.15 under wet condition for sawtooth pattern. In Figure 4.5(c), the maximum value of MAXSCRT is 1.0 for all three load patterns; means, both dry and wet samples shows damages. In Figure 4.5(d), the maximum value of MAXSCRT is about 0.13 under dry condition and about 0.18 under wet condition is about 0.18 for the triangular pattern; the maximum MAXSCRT value is about 0.21 under the dry condition and 0.30 under the wet condition for sawtooth load pattern; the maximum value reaches to 1.0 for rectangular pattern under both dry and wet conditions.