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Fracture, Fatigue, Failure and Damage Evolution, Volume 6 of the Proceedings of the 2018 SEM Annual Conference & Exposition on Experimental and Applied Mechanics, the sixth volume of eight from the Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on a wide range of areas, including:

Novel Experimental Methods

Extreme Environments

Interfacial Fracture

Integration of Models & Experiments

Mechanics of Energy & Energetic Materials

Integration of Models & Experiments

In Situ Techniques for Fatigue & Fracture

Microscale & Microstructural Effects on Mechanical Behavior

### Chapter 1. In Situ Strain Measurement in Solid-State Li-Ion Batteries

Volumetric changes due to repeated lithiation and delithiation are a significant source of electrode degradation and capacity fade in rechargeable batteries. Measurement of such volumetric changes and their resultant electro-chemo-mechanical strains and stresses have previously been investigated in conventional liquid-electrolyte Li-ion batteries. In the present study, we propose to extend the current knowledge and measurement techniques into the area of all-solid-state Li-ion batteries. Due to the presence of inherent property mismatch as well as confinements imposed at the interfaces between the electrodes and solid electrolyte, solid-state battery components are more prone to interfacial damage and. In this work, novel experimental approaches are designed to facilitate in-situ strain measurements on solid electrolytes (SE), electrodes and SE/electrode interface. Digital image correlation (DIC) is utilized to enable full-field strain measurements.
B. Koohbor, L. Sang, Ö. Ö. Çapraz, A. A. Gewirth, R. G. Nuzzo, S. R. White, N. R. Sottos

### Chapter 2. Crack-Tip Plastic Zone Size and Shape via DIC

In this paper Digital Image Correlation (DIC) is used to characterize the crack-tip plastic zone size and shape under plane stress and plane strain situations. For that, two disk-shaped tension DC(T) specimens made of 1020 steel with thicknesses 2 and 30 mm were used in fatigue crack growth tests to simulated plane stress and plane strain conditions, respectively. Fatigue cracks were grown under quasi-constant ΔK (stress intensity factor range) and stress ratio (R) respectively equal to 20 MPa√m and 0.1. A single 100% overload was applied when the crack reached a crack length of 6 mm (i.e. total crack length/specimen width = 0.3). Experimental measurements of the monotonic plastic zone at different stages during overload application are compared with finite elements simulations to predict the size and shape of the crack-tip plastic zone. A detailed discussion is given based on the DIC measurements obtained from the current investigation, including the experimental observations of crack closure.
G. L. G. Gonzáles, J. A. O. González, V. E. L. Paiva, J. L. F. Freire

### Chapter 3. Investigating Dynamic Fracture Parameters for Al7075-T651 Using Modified Hopkinson Pressure Bar (MHPB)

Dynamic fracture toughness of engineering materials is an important parameter in damage evaluation and safety assessment of the structures that are often subjected to impact loading. In the current work, dynamic initiation fracture toughness has been experimentally evaluated at different loading rates for a aluminium alloy Al7075-T651. It was observed that dynamic fracture toughness increases with the loading rates. The experimental set up used in this study is a Modified Hopkinson Pressure Bar consisting of the incident bar, a projectile, and a adjustable three-point bend fixture. Specimens used in the experiments are machined according to ASTM-E399 standard. Two different sets of experiments were conducted at projectile velocities of 12.7 m/s and 13.9 m/s with corresponding launch pressure of 1 bar and 1.5 bar respectively. Stress intensity factor was evaluated using a established load point displacement technique, while the time of initiation of fracture (tf) was obtained using a stereo-configuration of high speed cameras in conjunction with 3D Digital Image Correlation. The dynamic initiation fracture toughness was evaluated and was found to be 18.48 MPa$$\sqrt{m}$$ and 21.68 MPa$$\sqrt{m}$$ for the given boundary conditions respectively.
Sanjay Kumar, Anoop Kumar Pandouria, Vikrant Tiwari

### Chapter 4. Failure Testing Under In-Plane Biaxial Tension and Out-of-Plane Compression

The deformation and failure behavior of 2024 aluminum was investigated under combined in-plane equi-biaxial tension and out-of-plane compression. This loading configuration yields stress states of Lode parameter = −1 and triaxialities ranging from −0.67 to 0.17. Testing was performed using a variation of the standard ASTM quasi-static hemispherical punch test, with a reduced punch diameter and the addition of an annealed copper backing plate behind the specimen. The reported stress states at the failure point were then determined numerically using LS-DYNA.
Nathan Spulak, Robert Lowe, Jeremy Seidt, Amos Gilat

### Chapter 5. An Experimental Method to Induce and Measure Crack Propagation in Brittle Polymers with Heterogeneities

Facture mechanics of heterogeneous brittle solids is a field of active research due to the recent developments in additive manufacturing to fabricate components with complex engineered microstructures. The majority of experimental work in crack propagation uses data from a single plane, usually on free surfaces, to measure the displacement field around the crack and the crack tip location. These measurements are used to determine the crack tip fields and fracture toughness which provides insights about the failure of a material. However, it is well known from three dimensional theory and experiments that the crack front shape and stress distribution is not constant through the thickness of a specimen. When toughening heterogeneities are added to a material, the theories and mechanics become significantly more complex. To better understand these stresses and shapes for both homogeneous and heterogeneous materials, an experimental method has been developed to induce steady-state crack propagation in thin, brittle hydrogel polymers. A microfilament needle inserted into the specimens allows for fluid to enter the crack and exert pressure on the crack surface, which effectively wedges the crack open. Distributed fluorescent microspheres serve as a speckle pattern for Digital Volume Correlation (DVC) of volumetric images captured using confocal microscopy. The DVC displacement field allows for determination of the 3D crack tip fields. This study seeks to provide an enhanced understanding of the three dimensional nature of crack interactions with heterogeneities and renucleation events, which can significantly improve our ability to design material toughness.
Kimberley Mac Donald, Guruswami Ravichandran

### Chapter 6. The Sandia Fracture Challenge: How Ductile Failure Predictions Fare

The Sandia Fracture Challenges provide the mechanics community a forum for assessing its ability to predict ductile fracture through a blind, round-robin format where computationalists are asked to predict the deformation and failure of an arbitrary geometry given experimental calibration data. This presentation will cover the three Sandia Fracture Challenges, with emphasis on the third. The third Challenge, issued in 2017, consisted of an additively manufactured 316L stainless steel tensile bar with through holes and internal cavities that could not have been conventionally machined. The volunteer prediction teams were provided extensive materials data from tensile tests of specimens printed on the same build tray to electron backscatter diffraction microstructural maps and micro-computed tomography scans of the Challenge geometry. The teams were asked a variety of questions, including predictions of variability in the resulting fracture response, as the basis for assessment of their predictive capabilities. This presentation will describe the Challenges and compare the experimental results to the predictions, identifying gaps in capabilities, both experimentally and computationally, to inform future investments. The Sandia Fracture Challenge has evolved into the Structural Reliability Partnership, where researchers will create several blind challenges covering a wider variety of topics in structural reliability. This presentation will also describe this new venture.

### Chapter 7. Characterization and Modeling of Low Modulus Composite Patched Aluminum Center Crack Tension Specimen Using DIC Surface Displacements

Composite patch repairs of aluminum structures used in marine and aerospace industries are designed using closed form solutions assuming thin, plane stress, linear-elastic structures or numerical methods for repairs of thick aluminum. Both methods are based on linear elastic fracture mechanics and compare crack tip predictions to a critical strain energy release rate or stress intensity. Analytical and numerical predictions are reasonable for linear-elastic behavior, but these methods do not account for elastic-plastic behavior at the crack tip that initiates above the linear-elastic limit and continues until the ultimate load. This research used digital image correlation and finite element analysis to study the full field displacement and J-integral ahead of the crack tip for un-patched and patched center crack tension specimens loaded monotonically to failure. Free surface crack tip strain and J-integral behavior remained an intrinsic property of the aluminum directly related to the crack opening displacement (COD) and were independent of one sided composite patch reinforcement. However, the crack tip bending deformations induced by the patch reinforcement increased the COD by 20% over the un-patched behavior after patch failure, most likely due to observed changes in the formation of the plastic zone ahead of the crack. Comparison of test results and analytical predications indicated a significant difference between linear elastic and elastic plastic predictions beyond the linear-elastic limit highlighting the need to utilize elastic plastic fracture mechanics and the J-integral to optimize composite patched center crack tension specimens for ultimate load.
Daniel C. Hart, Hugh A. Bruck

### Chapter 8. Influence of the Temperature on Lifetime Reinforcement of a Filled NR

B. Ruellan, J.-B. Le Cam, E. Robin, I. Jeanneau, F. Canévet, F. Mortier

### Chapter 9. In-situ Crack Tip Stress Measurement at High Temperature in IN-617 Using Combined Nano-Indentation and Nano-Mechanical Raman Spectroscopy

In this work, the in-situ measurement of crack tip stresses in Inconel 617 at high temperature is presented. The temperature during loading in the current work was varied in the range from room temperature to 1073 K (800 °C). Three-point bending tests for in-situ notch tip stress measurements with increasing load were performed. A Combined Nano indentation and Nano mechanical Raman spectroscopy (NMRS) methods are used to measure notch tip plasticity induced stress distribution. Optical microscopy and SEM imaging is used to analyze the effect of surface finish and oxidation on the Nano indentation measurements. An in-situ Nano mechanical Raman spectroscopy is used to obtain the stress distribution at the notch tip during three point bending. The size resolution of measurements of notch-tip stresses was in the range of few microns. Temperature dependent (up to 1073 K) material properties were studied in terms of hardness and elastic modulus variation as a function of temperature. Microstructure dependent local mechanical properties were obtained using Nano indentation and is used in the finite element simulation. A finite element method based formulation to predict microstructure and temperature dependent crack tip stresses is presented and validated using the experimental stress distribution obtained from NMRS.
Yang Zhang, Chandra Prakash, Vikas Tomar

### Chapter 10. Modification of Benthem Solution for Mode I Fracture of Cylinder with Spiral Crack Subjected to Torsion

In this paper, a Benthem asymptotic solution is adapted and modified for a linear elastic fracture mechanics of a V-notch spiral crack. A spiral crack on a cylindrical sample is implemented to quantify the mode I fracture toughness of materials subjected to pure quasi-static torsion. The torque corresponding to fracture initiation is measured experimentally and used with a modifying Benthem solution to quantify the fracture parameter. A geometric factor for a cylinder specimen with a spiral crack on the surface is developed by finite element simulation. The proposed solution, along with stress intensity factor data of different materials, is presented here as a benchmark work. The results show that the proposed formula of the stress intensity factor for spiral crack cylinder specimen is in agreement with the other conventional methods, with an average error of less than 5%. The stress distribution and details of the experimental and numerical analysis are discussed.

### Chapter 11. An Investigation of Stress Concentration, Crack Nucleation, and Fatigue Life of Thin Low Porosity Metallic Auxetic Structures

This paper investigates, both experimentally and numerically, the mechanical response of low porosity thin metal samples under fatigue loads. The specimens, characterized by an overall porosity of 10%, were designed using selected patterns of voids and then fatigue tested to estimate the influence of both auxetic and non-auxetic tessellations on the mechanical performance. During the loading, detailed deformation maps were recorded by means of bi-dimensional Digital Image Correlation (DIC). The experimental data collected during this study indicate that the use of auxetic patterns could be a strategy to enhance the fatigue life of porous structures. In addition, DIC analysis is shown to be an excellent non-contact experimental method to assess the cumulative damage of the samples and to predict the crack starting points well before they are detectable by the unaided eye.
L. Francesconi, M. Taylor, A. Baldi

### Chapter 12. Cohesive Zone Smoothing of Bending Stiffness Heterogeneities in Tape Peeling Experiments

This work studies the interaction between the cohesive zone and elastic stiffness heterogeneity in the peeling of an adhesive tape from a rigid substrate. It is understood that elastic stiffness heterogeneities can greatly enhance the adhesion of a tape without changing the properties of the interface. However, in experiments performed on adhesive tapes with both an elastic stiffness heterogeneity and a substantial cohesive zone, muted adhesion enhancement was observed. It is proposed that the cohesive zone acts to smooth out the effect of the discontinuity at the edge of the elastic stiffness heterogeneities, suppressing their effect on adhesion. This work presents peel tests performed with heterogeneously layered 3 M 810 tape that demonstrate the muted enhancement. Additionally, numerical simulations further investigating the interaction between elastic heterogeneity and cohesive zone are presented.
Louisa Avellar, Tucker Reese, Kaushik Bhattacharya, Guruswami Ravichandran

### Chapter 13. Experimental Study on Fatigue Performance of Steel-Concrete Composite Girders

Besides the static load, the fatigue load caused by vehicles always exists in the bridge structures. This type of loading may cause failure even when the nominal peak loads are less than the ultimate capacity of the structure. In this paper, an experimental work, consists of two specimens, was introduced to study the fatigue behavior of shear connectors and steel-concrete composite beams. The fatigue tests were conducted under a four-point bending test with two different stress ranges in a constant amplitude. The testing measurements during the fatigue test included deflection, strain in the shear connectors, and slippage between the concrete flange and the steel beam. After completion of the fatigue tests, it was obvious that providing top and bottom longitudinal reinforcement as well as enough transverse reinforcement in the concrete flange can provide adequate confinement to concrete to limit fatigue cracks in the concrete flange. In addition, a growth in the cyclic deflection limits was obtained by increasing the number of cycles due to the damage region that developed in the concrete flange by the shear studs and caused a loss of stiffness in the shear connection.
Ayman El-Zohairy, Hani Salim, Aaron Saucier

### Chapter 14. Numerical Modeling of Charpy Impact Test to Determine the Fracture Characteristics of Aluminium Alloy 6061

Impact testing is commonly utilized to determine the fracture characteristics of engineering materials under dynamic loading. Materials have the tendency to behave differently under dynamic high rate loading as compared to their quasi static response. Additionally, impact testing can also reveal information about (i) a material’s resisting behavior to high rate loading, as well as (ii) the impact characteristics through measuring the energy consumed during the impact of notched test specimens. The current study incorporates a Johnson-Cook (JC) material constitutive law and failure computational model to simulate the Charpy test for Al-6061. The JC material model is generally employed to simulate the problems related to impact and penetration. The aim of this current study is to provide a numerical assessment tool using ABAQUS for the better and reliable predictions of impact behavior and to facilitate the design process. The numerical results were found in agreement with the experimental validations.
Salman Pervaiz, Sathish Kannan, Karthikeyan Ram, Wael A. Samad

### Chapter 15. A Progression on the Determination of Dynamic Fracture Initiation Toughness Using Spiral Crack

A recent development on identifying the static and dynamic initiation fracture toughness of materials by using a single v-notch spiral crack is presented. A polycarbonate solid cylindrical sample with spiral crack is implemented in this work to demonstrate the method. The quasi-static experiment was conducted by applying a pure torsion on the specimen using an MTS axial-torsion machine. The dynamic fracture experiment was conducted using Torsional Spilt Hopkinson Bar. In both cases, the torque corresponding to fracture initiation is measured experimentally and used as input to the numerical simulation. A new emphasis relation for a cylindrical specimen with spiral crack is also proposed and used with the experimental data to quantify the initiation fracture toughness. The results show that the spiral crack specimen is an effective method to determine the fracture toughness of materials.

### Chapter 16. Damage Evolution and Local Strain Redistribution in Composite Laminate with Various Fiber Arrangements

The initiation and gradual development of damage in composites is associated with the degradation of the composite laminate properties. Understanding the characteristics of damage evolution in composite laminates has been one of the major interest in composite studies. There is a lot of progress in this regard, however still there is a lack of clear understanding on how damages are initiated, grown and transformed from one form to another. In this study experiments are conducted to capture the strain localization and cracks formation on the free-edge of composite laminates. Laminates that have a stacking arrangement of (0/−Ɵ/+Ɵ/90)s with plies that have different fiber angles (Ɵ = 15°, 30° and 45°) are manufactured. Coupon samples are made from these laminates and subjected to a uniaxial tension loading until final fracture. Using digital image correlation technique at high magnification, the local deformation field is determined. From the test, it is observed that the strain/stress response of the composite is influenced by the arrangement of the fiber angle of the off-axis plies. From the strain contours obtained on the free-edge, the gradual initiation and growth of matrix cracks is observed to be localized in the 90° plies. In addition, these matrix cracks grow and lead to cause delamination between the 90° plies and neighboring plies. The local strains in each individual ply are seen to fluctuate along with the emergence of cracks at the vicinity of the damage as a result of stress redistribution.

### Chapter 17. Combined Modeling and Experimental Approach to Improve Mechanical Impact Survivability of GaN Power FET

An alternative approach was taken to improve the high-g shock tolerance of electronic devices. Rather than stiffening electronic devices with potting, the electronic device mass was reduced by an appropriate amount to match the compliance of the device to the circuit board. The devices studied were field effect transistors (FET) in bare die form factor and allowed a wafer thinning process to be utilized. A global-local finite element model was utilized to determine the ideal die thickness for matching the compliance. Test boards were populated with optimal thinned devices and stock devices for comparison on the same board. A three step thinning process was utilized in an effort to minimize the induced defects from the thinning process. The circuit boards with mounted FET’s were dropped from a shock drop tower to successively higher g-shocks up to 60,000-g. The electrical performance of each device was tested and verified after each level of mechanical shock. In general, most devices (both stock and thin) fail electrically before visual evidence of mechanical failure was present. The highest peak acceleration a device survived without failure is used as a figure of merit (e.g. the device failed on the next higher drop). The average of the “peak survived accelerations” for thinned devices is found to be about 25% higher for thin devices than for stock devices. However there was a wide variability in the results, which appears to be the greatest challenge to improving stock tolerance predictability and high confidence reliability of electronic devices.
John B. Ferguson, Sangwook Sihn, Albert M. Hilton, Curtis M. McKinion, Steven R. Dooley, Ajit K. Roy, Amanda M. Schrand, Eric R. Heller

### Chapter 18. Mechanics of Materials and Fracture for High School Students

We developed a nine session after-school curriculum to introduce high school students to fracture mechanics through interactive and hands-on experimental exploration of mechanics of materials and structures. Each session begins with a discussion of the week’s core concept in the context of a real world example of its application or importance. The remaining time is devoted to small group hands-on activities that reinforce and further explore the concept. The program revolves around the use of a custom designed portable load frame to perform material testing of 3D printed materials and structures. Students are introduced to the load frame during the second session where they determine material properties using a cantilever beam experiment. In the following sessions students focus on individual concepts in the experiment such as the source of the cantilever beam equation or dimensional analysis to determine the units of their results. The final three sessions involve bringing together all the concepts from the previous sessions to try to design the stiffest beam within a constrained cross-sectional area. Students go through the engineering design process from defining the problem to designing and testing prototypes to choosing a final design, 3D printing it, and testing it. Throughout the tests, they collect load and displacement data to calculate the achieved beam stiffness. Additionally, all beams are tested to failure to observe fracture mechanisms and ultimate strength. The primary goals for this program are to reinforce students’ prior knowledge from their science classes, demonstrate potential applications of additive manufacturing, and inspire interest in mechanics of materials.
Louisa Avellar, Kimberley Mac Donald