R-3 Repository :: Browsing by Author "Pharr, George M."

Browsing by Author "Pharr, George M."

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A finite element study of the effects of residual stress on conical indentation
(1993) Bolshakov, Alexei Olegovich; Pharr, George M.
The finite element method has been used to study the behavior of an aluminum alloy during elastic-plastic indentation by a rigid conical indenter to determine how the indentation process is affected by residual stress. The study was motivated by recent experimental results which showed that the hardness and elastic modulus of the alloy measured using nanoindentation methods appeared to decrease as the residual stress was increased. Biaxial radial stress was applied as a boundary condition, and indentation load-displacement curves were generated and analyzed according to various accepted methods for measuring hardness and modulus. The results of the study show that the standard methods by which hardness and elastic modulus are measured can lead to inaccuracies because they do not account for pile-up in the contact area calculations. Furthermore, if the contact area is measured properly, then hardness and elastic modulus are not significantly affected by residual stress.
A study of liquid enhanced creep in porous potassium chloride
(1984) Sheikh, Gholamreza; Pharr, George M.; Brotzen, Franz R.; McLellan, Rex B.
This research was a study of liquid enhanced creep in cold compressed potassium chloride whose grain boundaries were filled with saturated aqueous solution of KC1. This liquid was found to greatly accelerate the rate of creep in the material. It was found that two independent deformation mechanisms operate. The first occurs at low stresses (.163 MPa and below) and it is characterized by a linear stress dependence. The second mechanism dominates at higher stresses (.32 MPa and above), and is characterized by a stress exponent of two. The mechanisms are documented in terms of differences in volumetric strain behavior, creep ductility, and grain size dependence. It is suggested that the low stress mechanism is a diffusional one, similar to Coble creep with the liquid acting as a rapid diffusion path for transport of the solid. The high stress mechanism is not yet clearly understood, but is shown to involve grain boundary sliding accomodated by internal cavitation.
Application of numerical methods to dislocation modeling of creep
(1988) Tibbits, Patrick Allen; Pharr, George M.
Three computer simulations of dislocation mechanics models of fundamental aspects of creep predict certain creep behaviors of solids. The first two simulate the dynamics of infinite straight dislocations in two models of creep proposed by Weertmann as the solution of a set of coupled ordinary differential equations describing the x and y velocities of the dislocations as functions of their locations, applied stress, and glide and climb mobilities. Dual-order, error-estimating, adaptive stepsize Runge-Kutta methods of Verner and of Fehlberg are used to solve the systems of ODE's. Predictions for the behavior of the stress exponent as a function of stress and model geometric parameters differ from predictions obtained using original models. Stress exponents on the order of 5 to 6 are found to occur without assigning a stress dependence to microstructural parameters. The third simulation is of a subgrain (tilt) boundary modeled as a set of straight parallel vertically aligned edge dislocations which bow out under applied shear stress in a direction perpendicular to the plane of the boundary. The curved dislocations of the boundary are modeled as assemblies of finite straight segments using the expressions of Hirth and Lothe for stress fields of such segments. Equilibrium configurations of the boundary under increasing applied stress are found by minimizing the sum of the squares of the glide shear stress at each segment endpoint over the boundary configuration. Minimization is done with a multi-dimensional quasi-Newton secant method which employs the rank-1 update of Broyden. Stress is incremented until no equilibrium configuration can be found in order to find the maximum stress at which the boundary is stable (Orowan stress for the boundary). Stresses exerted within the subgrain by the stable boundary configurations are calculated, and this backstress is related to the magnitude of the applied stress. Backstress within the subgrain is concluded to be nearly linear in the applied stress, but may increase or decrease with applied stress at differing subgrain boundary tilt angles.
Effects of liquid phases on interfacial sliding in alkali halide crystals
(1989) Baykara, Tarik; Pharr, George M.
The effects of liquids on intrinsic interfacial sliding have been studied in NaCl crystals. The primary liquids in the study were water, methanol, and mixtures thereof. Sliding experiments were performed using a simple geometry in which a shear and normal compressive component of force were exerted on the interface. The geometry consisted of two single crystals joined at a boundary whose normal was inclined at an angle, $\theta$, to an axis along which a compressive load, P, was applied. The specimens were found to deform in two distinct ways: (1) by sliding along the interface, and (2) by indenting into one another in a direction normal to the interface. The introduction of liquids into the interface through channel-like defects was found to increase both the rate of sliding and indentation, with the increases being much greater for liquids with high water contents. It was found that the overall rate of displacement along the axis of the specimen was effectively independent of P but increased in roughly a linear fashion with $\theta$. A model for the process is developed in which displacement is produced primarily by interfacial sliding, with the liquid acting to promote the rate by undercutting the boundary and reducing the effective area of contact. The area of contact is determined by adaptations of friction theory, which lead to the observed P and $\theta$ dependence of the displacement rate. In addition, results of other experiments are presented which describe how grain boundaries in NaCl and KCl bicrystals are penetrated by water and methanol. Water is found to penetrate at much greater rates. This is discussed in terms of the differences in wetting and solubility exhibited by the two liquids. Both the sliding and penetration experiments are important in the understanding of liquid enhanced creep.
Factors limiting the accuracy of mechanical-property measurement by nanoindentation
(1997) Tsui, Ting Yiu; Pharr, George M.
Nanoindentation techniques have been widely used to measure thin film mechanical properties. One of the most commonly used methods of analysis of nanoindentation load and displacement data was developed by Oliver and Pharr. The objective of this dissertation is to examine some of the limitations of this method and develop improvements so that a more accurate hardness and elastic modulus measurements can be made. Detailed experimental studies of bulk monolithic materials and soft films on hard substrates were performed to evaluate the validity of the Oliver and Pharr experimental technique and analysis procedures. Three different indenters were used. They were the Berkovich and Vickers pyramids, and a cone with a 70.3$\sp\circ$ included angle. It is shown that there are inherent limitations in the Oliver and Pharr indenter shape-function calibration method which means that it cannot be applied to the blunt Vickers and conical indenters used in this work. A new procedure was developed which avoids these problems. The pile-up behavior of monolithic and thin film materials was extensively investigated. Experimental results for monolithic materials show that materials with low elastic modulus to hardness ratios (E/H) such as ceramics are less likely to pile-up. On the other hand, monolithic materials which have high E/H ratios and low strain hardening coefficients or soft films on hard substrates are more likely to pile-up. The pile-up generated during the indentation process in these materials can create as much as 50% more contact area between the indenter and the specimen. The effects of pile-up on the hardness and elastic modulus measurements for monolithic and thin film materials were examined. It is shown that when pile-up occurs, Oliver and Pharr method overestimates both the hardness and the elastic modulus. Only if these extra contact area generated by the pile-up is included are the correct hardness and elastic modulus values obtained. The amount of pile-up is also found to depend on the indenter geometry. The Vickers indenter generates more pile-up at the indentation corners than the Berkovich indenter for both monolithic materials and soft films on hard substrates. The absolute amount of pile-up in monolithic materials for Vickers indentations is also more than the Berkovich.
Fatigue analysis for non-normal stochastic stress
(1982) Hu, Sau-Lon James; Lutes, Loren D.; Merwin, John E.; Pharr, George M.
The basic goal of this study is to determine the relationship between the fatigue damage predicted for Gaussian and nongaussian processes when both are analyzed by the rainflow counting method. Due to a lack of references on nongaussian process simulation, some initial effort is devoted to finding a simple way of generating nongaussian processes. In this study, in addition to mean and variance (the usual two parameters of a normal distribution), kurtosis is chosen as a third parameter to indicate the degree of non-normality. A theoretical prediction of the fatigue damage due to a nongaussian process is also obtained for the special situation of a narrow-band process with the exponent in the S-N curve limited to integer values. The effect of non-normality on the empirical rainflow results (for any bandwidth process) is shown to be approximately the same as the effect predicted theoretically for the corresponding narrow-band process. A practical example associated with the fatigue life design of an offshore platform is given. It incorporates non-normality considerations into the design procedure. It is concluded that the effect of non-normality should not be neglected. It is also noted that the influence of nonnormality is affected not only by the kurtosis of the stress process, but also by the slope of the S-N curve (which is a material property).
Finite element studies of mechanical property testing by nanoindentation methods
(1996) Bolshakov, Alexei; Pharr, George M.
Nanoindentation is a widely recognized method for characterizing the mechanical properties of thin films and small volumes. This dissertation reports the results of finite element analyses of elastic and elastic-plastic indentation by a rigid cone aimed at improving methods for measuring of contact area, hardness and elastic modulus by nanoindentation methods. Analytical and finite element results are presented which show that corrections to Sneddon's solution are needed to properly describe elastic indentation by a cone. Since most nanoindentation methods are based on Sneddon's solution, these corrections have important consequences for making accurate mechanical property measurements. Elastic-plastic finite element simulations are presented which show that pile-up can significantly affect the accuracy of nanoindentation measurements. It is shown that an experimentally measurable parameter, the ratio of the final depth to the total depth of indentation, is useful in determining the amount of pile-up in the material. An investigation of plastic zones and stresses in indented materials reveals important correlations between them and the nanoindentation behavior of the material. Implications of these results for indentation cracking are also discussed. A long standing problem in nanoindentation is why load-displacement data obtained during unloading fit well to a power relation with a power law exponents in the range 1.25-1.50. Finite element simulations combined with elastic contact analyses are presented which provide a simple explanation for this behavior. General recommendations are made for improving of nanoindentation methods for measuring mechanical properties.
Selected mechanical problems in load- and depth-sensing indentation testing
(1999) Song, Haitao; Pharr, George M.
Indentation techniques are used extensively in mechanical property testing. In this dissertation, selected mechanical problems in load and depth sensing indentation testing are presented. One commonly used technique for determining a material's elastic modulus and hardness from indentation load-displacement data is the Oliver-Pharr method. In this method, radial displacements, pile-up and film-substrate interactions are not explicitly considered. Models to address the importance of these issues are developed and compared with the finite element analyses. Good agreement is achieved in many cases. An elastic solution for indentation of a monolithic material was developed by Sneddon in the 1950s. Analytical and finite element results are presented which show that modifications to Sneddon's solution are needed to describe elastic indentation accurately. Since most indentation methods for measuring mechanical properties are based on Sneddon's solution, these modifications have important consequences for making accurate measurements. A general modified formula is developed for an indenter whose shape can be described as a body of revolution of a power function. During the indentation process, samples plastically deformed by the indenter tend to pile up around the edge of contact. Pile-up can be a significant factor affecting the accuracy of indentation measurement. A new elastic-plastic model for conical indentation is presented which can increase the accuracy of the Oliver-Pharr method by accounting for this pile-up. The model is in good agreement with an empirical model proposed by Hainsworth and Page. Film/substrate interactions pose a particularly formidable problem in making indentation property measurements. In order to properly interpret experimental indentation data, an elastic solution for the film/substrate problem is highly desirable. However, an exact elastic solution is not available. In lieu of an exact solution, numerical methods and approximate methods are useful. A first order perturbation solution for the indentation of an elastic film on an elastic substrate is presented, the results of which are in good agreement with physical limits as well as with finite element results. Finite element analysis is a useful tool for studying elastic plastic indentation. With it, details of the indentation process which may be difficult to observe experimentally can be examined to gain insight into the mechanisms of contact. The finite element method has been used to examine the elastic-plastic behavior of a hard NiP film on a soft Cu substrate. The finite element results provide physical insight into unusual experimental behavior reported for this system.
Stochastic stress history simulation for fatigue analysis
(1983) Zimmerman, James J.; Lutes, Loren D.; Merwin, John E.; Bourland, Hardy M.; Pharr, George M.
The basic goal of this study is to find an alternate, more efficient method of simulating stochastic stress histories for fatigue analysis. Stress histories are generated from power spectral densities made up of either one or two rectangular blocks. The currently popular simulation technique produces a normal signal by summing sine waves with random phase angles. The fatigue damage predicted from stress histories simulated by this method is used as the basis of comparison for three other techniques. Two techniques which simulate correlated, Rayleigh distributed peaks and valleys are investigated. Another technique produces correlated peaks which have S. O. Rice's peak distribution. The rainflow method of cycle counting is used to determine the stress ranges from all the stress histories and Miner's rule is used to predict fatigue damage. It is concluded that fatigue damage from processes having single block power spectral densities can be efficiently and accurately predicted from a sequence of correlated peaks which have the peak distribution. This technique is three to four times faster than the currently popular technique. Simulation techniques which generate Rayleigh distributed peaks are found to be overly conservative in their prediction of fatigue damage. None of the three techniques investigated can be used for simulation of processes with two block power spectral densities. It is also concluded that a stress process cannot be sufficiently characterized solely by the spectral width parameter for fatigue damage predictions.
The hardness and modulus of molybdenum silicide/niobium microlaminates and stressed materials determined by nanoindentation
(1992) Tsui, Ting Yiu; Pharr, George M.
Nanoindentation techniques have been used to explore the hardness and elastic modulus of Nb/MoSi$\sb2$ microlaminates and stressed aluminium and stainless steel alloys. The elastic moduli of the microlaminates fall on the high end of range set by the rule-of-mixtures and increase slightly above it at small wavelengths. The hardness of the microlaminates increases with decreasing wavelength in a manner consistent with Hall-Petch strengthening. It is shown that average mechanical properties of the microlaminates can be measured when the plastic penetration depths are as small as one bilayer thickness. Studies in the aluminium alloy and stainless steel show that while hardness is affected by applied stress, the standard methods by which hardness and modulus are determined from nanoindentation data may lead to inaccuracies when large stresses exist in the material.
The hardness and modulus of molybdenum/aluminum oxide microlaminates as determined by nanoindentation
(1991) McAdams, Shaun Donald; Pharr, George M.
The elastic modulus and hardness of 1.2 $\mu$m thick films made of alternating and equal layers of sputter deposited Mo and Al$\sb2$O$\sb3$ were measured by a depth-sensing indentation apparatus which can test the properties of submicron volumes of material. Microlaminates with bilayer thicknesses ($\lambda$) of 5, 20, 30, and 100 nm were prepared and tested. The moduli of the microlaminates were found to follow a rule-of-mixtures. No "supermodulus effect" was observed. The hardness of the 100 nm microlaminate was observed to be almost twice as high as the hardness of either as-deposited Mo or Al$\sb2$O$\sb3$. This may be evidence of the "superstrength effect." A new method for determining the area of contact between an indenting diamond and the tested sample as a function of the plastic depth of indentation was established. An accurate area function is necessary for deriving mechanical properties from indentation data.

Browsing by Author "Pharr, George M."

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