The tensile yield strength of high-density polyethylene using instrumented indentation tests with a flat-ended cylindrical indenter was evaluated. The variation in the field expressed by stress and strain beneath the flat-ended cylindrical indenter is investigated using a new expanding cavity model to study the relation between tension and indentation. This model starts from the separation of forces into the compressive force on the material and the frictional one, which is generated during indentation on the sides of indenter. The authors propose a method to correct the frictional force based on the saturation of indentation hardening and obtain load–depth curve with compressive component only. For conversion of indentation force and displacement, our new representation model is applied. By modifying Johnson's model, the new assumption of conservation of indentation plastic volume is suggested. This model proves and supports conventional relations of the strain rates between indentation and tension theoretically. These are verified through the experiments: instrumented indentation and uniaxial tensile test. The authors find a good agreement between the tensile yield strengths at various strain rates.

Residual stress is generally evaluated using indentation by comparing the indentation curves of stressed and stress-free states. Here, we suggest a new method that can evaluate surface residual stress without indentation testing on stress-free specimen using stress-independent indentation parameters and an analysis of indentation contact morphology for the stress-free state. We found that several indentation parameters are independent of the stress by Vickers indentation testing on various stress states. The indentation contact morphology can be represented by indentation parameters including stress-independent ones, and by applying the stress-independent parameters obtained from the stressed state to the indentation contact depth function, we can estimate an indentation curve for stress-free state. The estimated curve matches well with the experimental stress-free indentation curve, and it was also confirmed that the applied stress values evaluated by comparing the estimated curve with the stressed indentation curve agree well with the reference values obtained from strain gauge.

We suggest a new method to evaluate stress directionality, the ratio of principal stresses, using nanoindentation by introducing a modified Berkovich indenter that is extended in one direction from the Berkovich indenter. In a nonequibiaxial stress state, the indentation load-depth curves are shifted differently as the extended axis of the indenter is placed in accordance with each principal direction. The indentation load-difference is proportional to each principal stress and the slopes are defined by the normal and parallel conversion factors whose ratio is constant at 0.58. The suggested method was verified by indentation tests using five nonequibiaxial stressed specimens. The evaluated stress directionality results show agreement with the applied reference values within ±20%. Furthermore, we calculated the conversion factor ratios for other modified Berkovich indenters extended to different degrees through finite element analysis and confirmed that the conversion factor ratio was inversely proportional to the extension of the modified Berkovich indenter.

The instrumented indentation test is an important alternative in quantifying residual stresses. Various indentation models have been developed to determine residual stresses, but no previous models can be applied to a nonequibiaxial residual stress state. To overcome this limitation, a Knoop indentation technique was developed to use the asymmetric characteristics of the Knoop indenter. With the ratio of conversion factors and equations for the relation between the load differences and the residual stress, a model of Knoop indentation was developed to determine the stress directionality p. This model was verified and compared through experiments on various biaxial tensile stress states. Imperfections in the Knoop tip change the conversion factor ratio. Using finite element simulations, this change in the conversion factor was expressed by a fitting equation.

We evaluate Vickers hardness and true instrumented indentation test (IIT) hardness of 24 metals over a wide range of mechanical properties using just IIT parameters by taking into account the real contact morphology beneath the Vickers indenter. Correlating the conventional Vickers hardness, indentation contact morphology, and IIT parameters for the 24 metals reveals relationships between contact depths and apparent material properties. We report the conventional Vickers and true IIT hardnesses measured only from IIT contact depths; these agree well with directly measured hardnesses within ±6% for Vickers hardness and ±10% for true IIT hardness.

We introduce a novel method to correct for imperfect indenter geometry and frame compliance in instrumented indentation testing with a spherical indenter. Effective radii were measured directly from residual indentation marks at various contact depths (ratio of contact depth to indenter radius between 0.1 and 0.9) and were determined as a function of contact depth. Frame compliance was found to depend on contact depth especially at small indentation depths, which is successfully explained using the concept of an extended frame boundary. Improved representative stress-strain values as well as hardness and elastic modulus were obtained over the entire contact depth.

Instrumented indentation testing (IIT) is a very useful technology for the mechanical characterization of materials. However, existing IIT techniques, which are based on the Hertz model and were developed for hard materials with negligible surface adhesion such as metals and ceramics, are difficult to directly apply to compliant materials such as elastomeric polymers which have viscoelastic hysteresis due to infinitesimal surface/interfacial adhesion. Here we employed some modified model to evaluate the work of adhesion in elastomeric polymer from our previous work, and reinforced our theory and algorithm through empirical approaches so as to consider the time-dependency of viscoelastic material as testing parameter. To do these all, we combined analytic JKR theory and conventional IIT technology to analyze the physical meaning of the theory and then verified our ideas experimentally with elastomeric polymer, PDMS (poly(dimethyl-siloxane)), of various compositions. Our algorithm was developed and verified on a microinstrumented indentation basis and extended even into the nanoinstrumented testing for the micro/nano-scaled applications.

Since in instrumented indentation the contact area is indirectly measured from the contact depth, the natural and unavoidable roughness of real surfaces can induce some errors in determining the contact area and thus in calculating hardness and Young's modulus. To alleviate these possible errors and evaluate mechanical properties more precisely, here a simple contact model that takes into account the surface roughness is proposed. A series of instrumented indentations were made on W and Ni samples whose surface roughness is intentionally controlled, and the results are discussed in terms of the proposed model.

Conventional nanoindentation testing generally uses a peak penetration depth of less than 10 % of thin-film thickness in order to measure film-only mechanical properties, without considering the critical depth for a given thin film-substrate system. The uncertainties in this testing condition make hardness measurement more difficult. We propose a new way to determine the critical relative depth for general thin-film/substrate systems; an impression volume analyzed from the remnant indent image is used here as a new parameter. Nanoindents made on soft Cu and Au thin films with various indentation loads were observed by atomic force microscope. The impression volume calculated from 3D remnant image was normalized by the indenter penetration volume. This indent volume ratio varied only slightly in the shallow regime but decreased significantly when the indenter penetration depth exceeded the targeted critical relative depth. Thus, we determined the critical relative depth by empirically fitting the trend of the indent volume ratio and determining the inflection point. The critical relative depths for Cu and Au films were determined as 0.170 and 0.173, respectively, values smaller than 0.249 and 0.183 determined from the hardness variation of the two thin films. Hence the proposed indent volume ratio is highly sensitive to the substrate constraint, and stricter control of the penetration depth is needed to measure film-only mechanical properties.

The fracture and fatigue properties of LIGA nickel MEMS structures were evaluated by microtensile and fatigue test methods. A microtensile/fatigue device was developed and specimens with feature size ten micrometers were used. The fatigue property was derived from displacement amplitude – the number of cycles to failure curve by applying a dynamic load with a piezoelectric actuator. The tensile/fracture properties after various cyclic loading were also measured. Both fatigue and tensile test results showed a cyclic softening phenomenon.

The height difference Δhb between the ideally sharp Berkovich indenter tip and a Δhb rounded tip was measured by direct observation using atomic force microscopy (AFM). The accuracy of the indirect area function method for measuring h was confirmed. The Δhb indentation size effects (ISE) in (100) single crystal copper, (100) single crystal tungsten, and fused quartz were characterized by applying the ISE model considering the rounded tip effect. The model fits the data these materials well, even though fused quartz does not deform by dislocations. However, a very small value of the ISE characteristic length h' was obtained for fused quartz. The present h' value for (100) copper is 32% larger than a previously-measured value for polycrystalline copper. This may indicate that grain boundaries suppress the dislocation activity envisioned in the ISE model.

Hardness and elastic modulus of micromaterials can be evaluated by analyzing instrumented sharp-tip-indentation load–depth curves. The present study quantified the effects of tip-blunting and pile-up or sink-in on the contact area by analyzing indentation curves. Finite-element simulation and theoretical modeling were used to describe the detailed contact morphologies. The ratio f of contact depth, i.e., the depth including elastic deflection and pile-up and sink-in, to maximum indentation depth, i.e., the depth measured only by depth sensing, ignoring elastic deflection and pile-up and sink-in, was proposed as a key indentation parameter in evaluating real contact depth during indentation. This ratio can be determined strictly in terms of indentation-curve parameters, such as loading and unloading slopes at maximum depth and the ratio of elastic indentation energy to total indentation energy. In addition, the value of f was found to be independent of indentation depth, and furthermore the real contact area can be determined and hardness and elastic modulus can be evaluated from f. This curve-analysis method was verified in finite-element simulations and nanoindentation experiments.

Polysilsesquioxanes (PSSQs) with the empirical formula (RSiO3/2)n have become very important as low-dielectric insulators for copper interconnects in the next-generation logic devices, but the detailed structure-property relationships were completely lacking. We have investigated the microstructure and functional properties of PSSQs with varying alkyl substituents and also PSSQ copolymers. As a result, significant advances have been made in the scientific understanding of PSSQ structures and significant improvements of key properties such as the crack resistance, mechanical modulus and hardness, and incorporation of nanometer-sized (<4 nm) porosity for ultra-low dielectric constants (<2.0).

Hardness and elastic modulus can be derived from instrumented sharp indentation curves by considering the effects of materials pile-up and sink-in and tip blunting. In particular, this study quantifies pile-up or sink-in effects in determining contact area based on indentation-curve analysis. Two approaches, finite-element simulation and theoretical modeling, were used to describe the detailed contact morphologies. The ratio of contact depth to maximum indentation depth was proposed as a key indentation parameter and was found to be a material constant independent of indentation load. In addition, this parameter can be determined strictly in terms of indentation-curve parameters, such as loading and unloading slopes at maximum depth and indentation energy ratio. This curve-analysis method was verified by finite-element simulations and nanoindentation experiments.

We used an electronic speckle pattern interferometer (ESPI) for nondestructive measurement in-situ displacement fields in microsystems. A four-step phase-shift technique and magnifier with long working distance were adopted to increase displacement resolution to ∼10−2 μm and spatial resolution to ∼2 μm. A thermal vacuum chamber was designed to induce thermal treatments, including annealing. From the identification of the residual-stress-free state, we quantitatively modeled thermal strains/stress fields, relaxation stresses during annealing, and residual stress fields. Thermoelasticity theory was applied to model the relationship between the relaxation stresses and the displacements measured by ESPI during the evolution of the residual-stress-free state. We assessed the surface residual stress fields of indented bulk Cu; a Fe-Ni lead frame of 100 μm width; and 0.5 μm Au film. In the indented Cu, the normal and shear residual stresses around the indented point range from –1.7 GPa to 700 MPa and –800 MPa to 600 MPa, respectively, and the residual stress in the bending area of the Fe-Ni lead frame was estimated at 148 MPa and verified using beam-bending theory. In the Au film, tensile residual stresses are uniformly distributed from 500 MPa to 800 MPa as verified by X-ray diffraction.

The nanoindentation technique has great promise in evaluating mechanical properties such as nanohardness and elastic modulus at micrometer or nanometer scales, since sample preparation and testing procedures are very easy. However, the nanohardness and elastic modulus cannot be directly related to basic material flow properties. Here a novel and simple experimental/computational method is proposed to extract stress-strain curves based on finite-element modeling (FEM) of nanoindentation. This method was verified for bulk Al by comparing the stress-strain curves extracted with those obtained from tensile testing, and was applied to Al thin films (0.5 μm and 1 μm) deposited on a Si substrate.

Tensile, fracture and fatigue properties of single- and polycrystalline silicon and LIGA-Ni were evaluated by the resonance frequency and microtensile methods. A new method for evaluating the fracture toughness that combines these two methods was proposed. A pre-crack was generated in an electrostatically driven test specimen and a load was applied by piezoelectrically driven microtensile equipment. Before the microtensile test, a new surface micromachining technique including a two-step sacrificial layer removal was used. The pre-cracked specimen was attached to microtensile equipment by a UV-adhesive glass grip. The fatigue pre-crack was successfully introduced and the fracture toughness could be derived on the basis of fracture mechanics. The fracture toughness of the pre-cracked specimen was relatively low compared with that of the notched specimen, so that we were able to determine the effect of the notch tip radius. The fatigue properties of LIGA-Ni film were also evaluated. A tensile-tensile fatigue load was applied by a piezoelectric actuator, and real-time load-displacement curves were displayed via computer. The dependence of S-N curves, crack propagation rates and fatigue-notch factor on the applied load for 10 μm Ni film was analyzed.

Residual stress in a thin film was analyzed by the nanoindentation technique. Two dominant effects of residual stress to indentation were summarized as the slope change in loading curve and the invariant value of intrinsic hardness. A stress-sensitive reversibly deformed zone around contact was modeled to explain the indentation behaviors under a residually stressed state. Finally, the residual stress was evaluated from the changes in contact shape and applied load during stress relaxation under the condition of constant indentation depth. The residual stresses in diamond-like carbon and Au films analyzed from this model agreed well with the average values measured by the curvature method.

Based on the identification of the residual stress-free state using electronic speckle pattern interferometry (ESPI), we modeled the relaxed stress in annealing, the thermal strain/stress and the residual stress field in case of both single and film/substrate systems by using the thermo-elastic theory and the relationship between relaxed stresses and displacements. Thus we mapped the surface residual stress fields on the indented bulk Cu and the 0.5μm Au film by ESPI. In indented Cu, the normal and shear residual stress are distributed over -800 MPa to 700 MPa and -600 MPa to 600 MPa respectively around the indented point and in deposited Au film on Si wafer, the tensile residual stress is uniformly distributed on the Au film from 500 MPa to 800 MPa. Also we measured the residual stress by the x-ray diffractometer (XRD) for the verification of above residual stress results by ESPI.