Observations of Failure Phenomena in Periodic Media

Introduction

Fracture Mechanics

The stress in zones of length s at the crack tips is limited to the yield strength of the material, σ0. The yield zone is larger because load discontinuity must be considered by limiting the stress to the yield strength of the material (the area between the solid horizontal line, σ0, and the dashed line).

Figure 1.1: a. Edge-cracked plate with applied load P (per unit thickness), displace- displace-ment v, and initial crack length a; b

Heterogeneous Fracture Mechanics

Instead, if E1>>E2, as in the case of a crack propagating from a hard material to a soft material, its strength increases, amplifying the strength of the singularity and driving the crack forward. Taking advantage of developments in additive manufacturing that allow parts to be printed with variable material properties, Weng and Xia performed fracture experiments on heterogeneous materials and found increases in toughness consistent with numerical simulations performed on the same [37].

Tape Peeling

The work done as a result of peeling the tape is equal to the peeling force times the distance over which it moves. Kendall varied the moment of inertia by alternately making the tape thicker (I = bd123, where b is the width and thickness of the tape).

Outline

When the load reaches a critical value, the crack propagates, resulting in failure of the material. On the reverse side of the heterogeneity (step down), the strain experiences an abrupt decrease to a value below the stable value of tear-off force associated with the tear-off of a homogeneous band, (1);

Toughening Mechanisms in Periodic Layered Media

Component Homogeneous Material Properties

Tensile testing is performed to determine Young's modulus and Poisson's ratio of Polyjet VeroBlackPlus (same as Vero except a different color) and DM8530 materials. Young's modulus using the linear region is the value used in the following work (Table 2.2).

Figure 2.1: Stress versus strain plots of ASTM D638 dogbone tests of VeroBlack- VeroBlack-Plus

Heterogeneous Bricks

A fresh razor blade is pressed into the tip of the notch to a depth of 1.3 mm to ensure an initial sharp crack. A camera pointed at a face of the sample speckled for DIC analysis begins acquiring images at the same time as loading. The crack front is assumed to be straight through the material; that is, the crack front visible on the surface is the length of the crack front through the inside of the sample.

The matrix between the inclusions in front of the crack appears to carry considerably less strain. However, it is difficult to draw definitive conclusions from this experiment due to the limitations of the experiment. Furthermore, the samples were small relative to the size of the heterogeneities, so edge effects could have significantly influenced the result.

Figure 2.3: Front view of fracture specimen with brick architecture. Design studies vary lengths (a), (b), and (c)

Heterogeneous Plates

In the plates with unfilled holes, the crack initially propagated horizontally through the remaining ligament of material between the tip of the original crack and the next hole in the material. Then the load continues to increase (much higher than the previous maximum), until it reaches a new maximum and the rest of the ligaments fail all at once. For both plates, the calculated critical stress intensity factor, K, is much lower for failure of the first ligament (with the notch) than for the second ligament (without the notches).

The strain in the y direction, y y, is calculated by dividing the applied displacement by the height of the specimen. Figures 2.11 and 2.12 show the individual components of deformation and von Mises stress in the undeformed configuration at the maximum load in the experiment. However, stains on the sample surface for DIC obscure the color of the material.

Figure 2.8: a. Schematic of the infinite strip fracture specimen b. Schematic of the of experimental setup.

Heterogeneous Stripes

Assume that as a result the material will fail at the fracture toughness of the Vero material, using the relationship between the energy release rate,G, and the critical stress intensity factor,KIc,G= KE2, and Eq. 2.7) for the critical applied force gives: For the 2, 4, 6 and 10 layer specimens, the final depth of the front crack is achieved by pushing a razor blade into the notch. Local pixel clustering is a technique that uses smaller subsets of the data to effectively degrade data while better preserving local structures.

One of the possible reasons for the discrepancy is that Euler-Bernoulli beam theory is not applicable to the compact tension specimen because the 'beams' are not slender enough. Fracture surface of HH-0616-10-1 showing a crack that started and stopped from the lower right edge and another crack that starts where it ends and spreads through the rest of the specimen. There may be some error with the large number of layers due to the size of the layers being comparable to the resolution of the DIC in the experiments.

Figure 2.14: Difference in fracture force between a double cantilever beam with two horizontal layers and one with twenty horizontal layers in each beam versus volume fraction of Vero.

Conclusion

After propagating through the front of the heterogeneity (step-up side), the tape returns to the stable peel force (1) in the region of increased (multi-layer) thickness heterogeneity; To study the origin of the valley in the peeling force (lowest value), it is interesting to consider the brittle case (no cohesive zone). The load starts to increase and the size of the cohesive zone increases as the crack front reaches the heterogeneity at B-C.

The load peaks at C, and the cohesive zone has penetrated well into the heterogeneous region of the tire. The onset of the cohesive zone size increase varies with the size of the cohesive zone. The influence of the shell front penetration (and subsequent involvement of more of the heterogeneity while changing the radius of curvature of the shell) is a contributing factor to the smoothing process.

Figure 2.19: Full-field strain components obtained using DIC prior to failure for a.

Crack Renucleation and Propagation in Periodic Layered Media . 40

Evaluation of Fracture Toughness in Homogeneous Materials

A great deal of information about fracture can be determined from observations of the fracture surfaces after material failure using fractography. Quantitative fractography is used to determine the fracture toughness of VeroBlack-Plus, the stiffer of the constituent materials. Compliance is calculated by measuring the slope of the displacement versus load plots, excluding the initial load toe.

The exact measurement of the length of the initial crack is taken after specimen failure using calipers from the failure surface. The initial sharp crack front is obtained by pressing a fresh razor blade into the specimen to a depth of at least the width of the initial notch. The exact measurement of the total length of the initial notch is taken after specimen failure using calipers on the failure surface.

Table 3.1: Flaw dimensions and mechanical and fracture properties of VeroBlack- VeroBlack-Plus

Renucleation and Toughening

A crack is introduced on the left side and the surf boundary condition drives the crack towards. Recall Zak and Williams' analysis of singularity strength at a crack tip near the interface of two materials from Section 1.2 [36]. The additional toughness is the difference between the toughness of the layer with and without the channel containing the crack.

Crack propagation measurements are determined post-test by manually locating the crack tip in each of the images. An early experiment imaged the samples without DIC speckle pattern and the results showing the crack stop locations and slow propagation are shown in Figure. The outliers are related to the fact that the crack does not propagate smoothly (usually the first or second step) or to the fact that there are few points (< 10) available for the calculation.

Figure 3.5: a. Periodic layered media without spine; b. Periodic layered media with spine

Discussion

The average value of bark strength in this region is used to normalize the results. The width of the cohesive zone can also be observed to vary in these images. The lower part of the strip and the upper part of the cohesive layer are connected using a connecting constraint.

The peel force reaches a steady state value in the homogeneous portion of the tape as it approaches the heterogeneity at A in Fig. The size of the cohesive zone takes two constant values during crack propagation related to the thickness of the band above the crack front. There is a correlation between the size of the initial cohesive zone and the onset of peel front penetration in the heterogeneous region;.

Figure 3.13: Crack propagating through layered stripe specimen. The forward-most point of the crack is marked with an arrow and considered as the crack tip.

Process Zone Smoothing of Heterogeneous Effects in Tape Peeling 64

Experimental

The initial strip length from the substrate to the grip is long enough so that the change in peel angle during peeling is minimized. The tape is left for at least 20 minutes before the start of the peeling test to ensure adhesion stability [79]. As the leading edge of the strip shell approaches the heterogeneity, the load increases and peaks when the shell front reaches the step up into the heterogeneity;.

The load begins to increase at B, but at C the adhesive bond of the heterogeneity to the base layer fails, resulting in a visible gap between the base layer and the heterogeneity. Because there is no obvious valley (lowest value) in these experiments, it is desirable to determine whether the brittle case is unaffected by a decrease in film thickness (i.e., the peel front propagates with constant force through the step-down interface) or if the strain actually drops abruptly , but this behavior is obscured by the fact that the peeling front rapidly propagates all the way through the heterogeneity to the step-up of the next one. The tape (2 cm wide) was formed by gluing a second layer of the same thickness of PET to the base layer using a UV curable super glue.

Figure 4.1: a. Tape peeling experiment configuration; b. Close up view of the heterogeneities.

Simulation

Peel strength and cohesive zone size are plotted as a function of time (applied vertical displacement). The charge decreases rapidly as the front reaches the other side of the heterogeneity at E-F and the charge is again. The size of the cohesive zone does not begin to increase until the peel strength has reached approximately half of its maximum value.

In the simulations, as the crack approaches heterogeneity, it becomes stuck and the strain starts to increase, while the cohesive zone remains the same size or decreases slightly. At a certain load before the peak, the size of the cohesive zone begins to increase, which coincides with the beginning of the penetration of the flaking front into the heterogeneous region. However, the onset of the increase in the size of the cohesive zone also depends on the adhesion strength, and lower values of the adhesion strength correspond to earlier onsets of penetration into the heterogeneous region.

Figure 4.7: Peeling of a PET/epoxy tape from an acrylic substrate with a step down heterogeneity; a

Discussion

Stress fluctuation, crack renucleation and hardening in layered materials”. Journal of the Mechanics and Physics of Solids (2018). Yield of steel plates containing crevices. Journal of the Mechanics and Physics of Solids pp. Cohesive Fracture of Elastically Heterogeneous Materials: An Integrative Modeling and Experimental Study. Journal of the Mechanics and Physics of Solids pp.

Homogenization and Path Independence of the J-Integral in Heterogeneous Materials”.Journal of Applied Mechanics issn: 0021-8936. Revisiting Brittle Fracture as an Energy Minimization Problem”.Journal of the Mechanics and Physics of Solids str. Numerical Experiments in Re-visited Brittle Fracture”.Journal of the Mechanics and Physics of Solids str.

Figure 4.12: Normalized peel force and cohesive zone size are plotted as a function of time for δ f = 0.05, a-d: G = 12.5, 25, 50, and 100 N/m

Summary and Future Work