mechanical characterization of damage and failure in

Introduction

Motivation

Sandwich structures can also be tailored to specific applications by combining different faceplates and core materials. An area of great potential interest for sandwich structures as structural materials lies in marine structures.

Review

Cellular Materials
Composite Materials

The disadvantage of the Tsai-Wu model is its dependence on a single coefficient of the multi-axial strength of the material. The study concluded that the strength of the composite is inversely proportional to the species volume.

Approach and Objectives

Longitudinal (cd) and shear (cs) wave speeds can be used to determine two elastic constants, Young's modulus (E) and Poisson's ratio (ν), for linearly isotropic, homogeneous materials, assuming that the density (ρ) of the material is known independently. Schematic of the finger used in the high strain test: (a) front view and (b) side view.

In Situ Characterization of Damage in

Introduction

The research on the accumulation of damage and the failure behavior of cellular materials relies on mechanical testing and postmortem evaluation of the outer surfaces of cellular samples. The results of the experiments carried out on the foam samples using the ultrasonic technique are then presented together with the proposed failure mechanisms responsible for the macroscopic observations.

Materials

This chapter is structured as follows; first the material used in the study is described, followed by an introduction to the ultrasonic method developed for the in-situ investigation of foams. The results of these tests are then discussed in relation to the results previously found using the ultrasound technique.

Table 1 lists the data for selected physical and mechanical properties found on the DIAB website

Ultrasonic Characterization Technique for in-situ measurement

The pulse echo (PE) mode is one of the most popular methods for measuring the speed of sound waves. This presents some difficulties in the placement of the transducers because the transducers themselves have finite dimensions.

Experimental Procedure

This wave splitting occurs due to mode conversion of the incident shear wave (SV) due to the coupling used between the pulser and the spacer. The discovery of the wave splitting and the resulting simultaneous measurement of the longitudinal and shear waves is described in the next section.

Figure 2.5. Loading fixture and protective housing of ultrasonic transducers for in-situ measurement of wave speeds while subjecting the specimen to uniaxial compression

Simultaneous Measurement of Longitudinal and Shear

The total longitudinal transit time of the longitudinal wave through the spacers and the sample, tdtotal, is shown in Figure 2.9. The total longitudinal transit time measured by the shear transducers was then compared to the longitudinal transducer measurement of the transit time of the longitudinal wave in the sample alone.

Figure 2.6. Input signal from a shear transducer and output signals of the longitudinal and shear receiving transducers from experiments on aluminum are plotted as a function of time

Experimental Results and Discussion

The transit times of the longitudinal and shear wave in the sample are calculated using Eqs. A contour plot of the Mises stress in the finger during loading is shown in Figure. The effect of confinement on the axial stress-strain curve of the material is illustrated in Figure 2.

A graph of the axial stress as a function of the longitudinal confining stress is shown in Fig. This demonstrates that the transverse stress has a much greater effect on the axial strength of the material. The graph shows that the longitudinal restraint does have an effect on the transverse stress of the material.

Figure 2.13. Young’s modulus, shear Modulus and Poisson ratio for Polycarbonate during Uniaxial Compression

Modeling for cell failure

Digital Image Correlation

Digital Image Correlation Algorithm

When the sample is compressed in the axial direction, the fingers of the clamp effectively "restrain" the sample in the longitudinal and transverse directions of the fibers. The data presented in the previous section showed that increasing the longitudinal restraint had little effect on the transverse strength of the material. The effect of confinement and strain rate on the maximum axial stress (transverse strength) of a composite.

The transverse confining stress had a much greater effect on the axial strength of the material compared to the longitudinal confining stress.

Figure 2.28. Experimental set up for the Digital Image Correlation (DIC) measurements

Digital Image Correlation Results

Summary

Schematic of the isolation device used in the dynamic test to introduce different levels of closure. Photograph of the isolation device used in the dynamic test to introduce different levels of closure. The graph shows that increasing the longitudinal restraint has little effect on the axial strength of the material.

The figure indicates that the longitudinal stress does not have a major influence on the axial strength of the material.

Characterization of Composite Materials

Introduction

Transverse loading refers to loading that occurs in the fiber plane and perpendicular to the fiber axes. Similarly, high strain rate testing also applied a series of confinements to the sample with a fixture that could measure the three major stresses in the material. The experimental results indicate that the mechanical response and strength of the composite in the transverse direction are functions of the strain rate and are mainly determined by the properties of the matrix material.

The consequences of this deviation in the orientation of the failure bands from the maximum shear trajectories at 45 degrees will be discussed in terms of confining stress and strain rate.

Material

The axis parallel to the fiber direction is defined as the longitudinal axis, the axis perpendicular to the longitudinal axis and parallel to the fiber plane is defined as the transverse axis, and the axis perpendicular to the fiber plane is defined as the transverse out-of-plane axis or axial direction (Fig. 3.3). The samples had to be prepared to the same specifications before they could be tested. The preparation process began with a large rectangular section cut from the base material using a band saw, parallel to the fiber direction to ensure that the fibers were longitudinally aligned.

Next, a cutting saw was used to cut the machined rectangle to the final sample size.

Figure 3.2. Schematic of specimen indicating its length width and height

Failure Models

For example, consider uniaxial stress in the fiber direction, where σ1 will be equal to T11 the longitudinal tensile strength of the composite and σ2=σ6=0. The previous section discussed how varying the finger material varied the inclusion on the samples, by suppressing expansion in the longitudinal and transverse fiber direction of the sample. The transverse strength of the material is seen to increase with longitudinal restraint strength, as illustrated in Fig.

Post-test inspection of the specimens revealed shear failure planes at ~50o to the longitudinal surface. Within the range of the experimental error, one can say that (i) the effect of strain rate on. In the case of plastic collapse behavior, it was expected to show uniform cell deformation.

Table 3.1. Tensile and compressive strengths of S2/8552 composite in the fiber and transverse fiber directions

Low Strain Rate Experimental Set up

High Strain Rate Experimental Set up

Confinement

Low Strain Rate confinement method

Varying Confinement with polycarbonate Pads Inserts . 84
Indentation

High Strain rate Confinement method

Schematic of the layered structure of the specimen and definition of the stress axis 3.6.1 Low strain rate confinement method. As the thickness of the pad increased, the length of the aluminum finger decreased and so did the overall confinement of the sample. The finite element calculations monitored the stress and strain of the finger at two different locations.

Item no. 38 corresponds to the stress at the finger-sample interface; item no. 3 corresponds to the location of the voltage meter.

Figure 3.9. (a) Photograph of the quasi-static confinement fixture; (b) Schematic of the top view of the confinement fixture used for the quasi static test to introduce lateral confinement

Experimental Results for Low Strain Rate Tests

The data show that the transverse confining stress does not change with confining in the longitudinal direction. Furthermore, the constraint in the longitudinal direction is an order of magnitude smaller than the limiting stress in the transverse direction. The test results were classified according to the material used in the toe in the longitudinal direction.

The resulting axial stress deformation curve without limitation in the longitudinal direction can be seen in fig.

Figure 3.26 Typical result of typical nominal stress strain data from a quasistatic test conducted at 0.001/s

Microstructural Characterization

The SEM micrograph on the right provides a more magnified view of the sample region indicated by the red box in Fig. As the magnification of the failure plane increases further, the failure features become apparent. It shows that there are two small cracks growing perpendicular to each of the failure bands.

However, this crack can be followed to its starting point and a 14640X micrograph (Fig. a) Image of the specimen confined by aluminum; (b) SEM micrograph of 5 mm.

Figure 3.40. (a) Photograph of specimen with aluminum finger longitudinal confinement and aluminum finger transverse confinement

High Strain Rate Results

The applied force is indicated by the arrows on the right side of the pattern, and the left and bottom sides of the toes were modeled as being on rollers. This means that the voltage meter reads a lower voltage than the actual voltage on the sample. To correct for this, the measured strain must be multiplied by 2.41. a) Missed drawing of the stress contour on the side view of the deformed section of the finger, (b) graph of the axial stress in element no. 37 and element no. 28, the locations of which are marked in (a).

This result agrees with the results of the low strain rate tests, which showed a much greater dependence of the transverse strength on the axial strength of the composite.

Figure 3.48. Schematic of the finger used in the high strain rate test: (a) front view and (b) side view

Strain Rate Effect

Summary

The confinement force on the specimen was a reaction force to the axial load of the material and not an applied force. For this reason, the experimental apparatus failed to explore the behavior of the composite material under large longitudinal confinement. The second half of the thesis focused on the failure behavior of S2-8552 glass/epoxy composite under multiaxial loading.

The digital image correlation method can be valuable for monitoring the behavior of foam attached to faceplates during deformation.

Conclusions

Summary

Foam
Composites

The stress-strain response results of the experiments indicated that the cell wall thickness controlled the failure behavior of the material. Knowing the two potential local failure modes, predictions of the global failure behavior for each were developed. Based on the orientation of these bands, a Mohr–Coulomb failure criterion seems appropriate to describe the transverse failure of the composite.

This study introduced several new experimental methods which made it possible to investigate the mechanical behavior of foams and composite materials in more detail.

Recommendations for Future Work

Ship System Limitations and Operational Requirements”, Proceedings of the Fifth Symposium on Naval Structural Mechanics, p.19 (1967). An Investigation of Mechanical Properties of Materials at Very High Rates of Loading", Proceedings of the Royal Society of London Series B62, 62: pp. Multiplying the stress by the Young's Modulus of the finger (Efinger) gave the stress in the finger, as shown in equation B below.

In order to accurately calculate the stress in the finger, ultrasonic measurements were used to determine the Young's modulus of the finger (Efinger,).