Fixture Compliance Research Articles

A method for accounting for test fixture compliance when estimating proximal femur stiffness

Fracture testing of cadaveric femora to obtain strength and stiffness information is an active area of research in developing tools for diagnostic prediction of bone strength. These measurements are often used in the estimation and validation of companion finite element models constructed from the femora CT scan data, therefore, the accuracy of the data is of paramount importance. However, experimental stiffness calculated from force–displacement data has largely been ignored by most researchers due to inherent error in the differential displacement measurement obtained when not accounting for testing apparatus compliance. However, having such information is necessary for validation of computational models. Even in the few cases when fixture compliance was considered the measurements showed large lab-to-lab variation due to lack of standardization in fixture design. We examined the compliance of our in-house designed cadaveric femur test fixture to determine the errors we could expect when calculating stiffness from the collected experimental force–displacement data and determined the stiffness of the test fixture to be more than 10 times the stiffness of the stiffest femur in a sample of 44 femora. When correcting the apparent femur stiffness derived from the original data, we found that the largest stiffness was underestimated by about 10%. The study confirmed that considering test fixture compliance is a necessary step in improving the accuracy of fracture test data for characterizing femur stiffness, and highlighted the need for test fixture design standardization for proximal femur fracture testing.

Effect of fixture compliance and cutting conditions on workpiece stability

This paper computes and investigates the effect of fixture compliance and cutting conditions on workpiece stability and uses it as a basis for selecting a suitable fixture among several alternatives. We use two criteria, the minimum eigenvalue of the fixture stiffness matrix and the largest displacement of the workpiece due to the cutting forces to assess the stability of the workpiece. First, the minimum eigenvalues of the fixture stiffness matrices, for the fixtures being considered, are computed. Second, since the eigenvalues are not dependant on the cutting forces, a displacement measure, the largest displacement of the workpiece due to the cutting force, is computed for each fixture. This displacement is a function of the cutting force and the fixture compliance. The choice of fixture is often a compromise between the two criteria. We also consider the combined influence of fixture compliance and cutting conditions on workpiece stability. The results from the simple study used for illustration show that the eigenvalues remain constant under different cutting conditions whilst the largest displacement reduces by 68%, a significant reduction.

Influences of Friction, Geometric Nonlinearities, and Fixture Compliance on Experimentally Observed Toughnesses from Three and Four-point Bend End-notched Flexure Tests

Three and four-point bend end-notched flexure tests, comprising a number of different test geometries, are performed on two different graphite/epoxy composites, and the toughnesses are obtained by a compliance calibration method of data reduction. The coefficient of friction along the crack plane and the flexural modulus of each material are then determined experimentally and used with nonlinear finite-element analyses to simulate these same test configurations. By using the mean experimentally observed critical load, these simulations are used to obtain the materials' toughnesses by three different methods. The first uses a previously developed `direct energy balance approach,' which is assumed to produce the `true' toughness. The second is by a simulated compliance calibration procedure, which is used to obtain the perceived toughness for an infinitely stiff fixture. In the third approach, experimentally determined fixture compliances, as a function of the test geometry, specimen, and crack length, are used along with the simulated compliance calibration procedure to obtain a perceived toughness that accurately accounts for the effects of friction, geometric nonlinearities, and fixture compliance. The perceived toughnesses as obtained by these simulations are shown to accurately recreate the perceived values of toughness that are obtained from the physical tests. Moreover, the finite-element simulations indicate that the true toughness values are essentially constant for a given material, and that the three-point bend end-notched flexure test will provide perceived toughnesses that correspond quite closely to the true value, whereas the four-point bend test often will not. For these reasons, the three-point bend configuration was found to be the more preferable of the two tests.

Effects of Friction, Geometry, and Fixture Compliance on the Perceived Toughness from Three-and Four-Point Bend End-Notched Flexure Tests

Linear and nonlinear finite element analyses are used to examine the effects of friction, test geometry, and fixture compliance on the perceived toughness as obtained from threeand four-point bend end-notched flexure tests. To this end, a newly developed ‘direct energy balance approach’ is used to obtain the ‘true’ energy release rate for any given specimen, test geometry, and coefficient of friction. Finite element analyses are also used in a simulated compliance calibration technique, which is combined with experimental results from fixture compliance tests to obtain a perceived toughness, i.e., the value that would be obtained by experiment. By varying the different parameters, the individual and combined effects of friction, test geometry, and fixture compliance on the ratio of the perceived to true toughness is obtained. The approach is applied to two graphite/epoxy materials for which toughnesses by the three(3ENF) and four-point bend end-notched flexure (4ENF) tests are obtained experimentally for a range of geometries. These experiments produced larger perceived mode II toughnesses, GIIc, by the 4ENF than the 3ENF test, and GIIc values from the 4ENF test were observed to decrease with increasing outer span length. The finite element simulations were shown to accurately recreate the perceived values of GIIc obtained from these tests. Moreover, the finite element simulations indicate that the true toughness values are essentially constant for a given material. These findings are used to make some general recommendations for choosing 3ENF and 4ENF specimen and test geometries, as well as to discuss the relative advantages and disadvantages of the 3ENF and 4ENF test methods.

Effect of Fixture Compliance on Thermally Enhanced Edge Registration in Microlamination

Microlamination involves the patterning, registration, and bonding of thin layers of material, called laminae, to produce highly paralleled, spatially intensified microchannel systems for the bulk processing of mass and energy. A Thermally Enhanced Edge Registration (TEER) technique has been developed for precision aligning large numbers of laminae in diffusion-bonding processes based on the differential thermal expansion between the laminae and bonding fixture. However, fixture tolerances necessary to promote buckle-free TEER bonding have been found to be very small (below 10 μm). This research focuses on the development of a new approach to thermal registration based on fixture compliance to permit looser fixture tolerances. An analysis based on both fin-buckling behavior and the compliance of the fixture is implemented to investigate the tolerance limit of a compliant TEER fixture. Experiments are conducted to verify the theoretical model. Results show that a compliant fixture can permit an acceptable tolerance limit in TEER.

Buckling Response of Transversly Loaded Composites Shells, Part 2: Numerical Analysis

The response of transversely point-loaded composite shells is investigated via the finite element method. The thin, circular cylindrical shells are hinged at a fixed distance apart on the straight edges and are free on the curved edges. Stability issues are considered, including nonlinear prebuckling, limit points, bifurcation, and postbuckling. In the finite element formulation, a novel technique is utilized to identify and traverse bifurcation points efficiently in the nonlinear elastic response. A classic shell buckling benchmark problem is solved here correctly for the first time; previous studies have found the isotropic shell to have a limit point, when, in fact, the shell bifurcates before reaching a limit point. Predicted results for graphite/epoxy laminated shells are in excellent agreement with measured load-deflection and mode-shape evolutions as previously reported. Two cases of extraordinarily good agreement between the data and model, particularly large-deflection asymmetric deformations modes through a bifurcation point and far into the postbuckling regime, clearly establish validated new benchmarks. Asymmetries in both directions of the shell plane, relative to the centrally applied point load, are discussed with regard to bifurcation and material couplings in the composite laminate. Asymmetric stress distributions are discussed in the context of composite damage resistance and previous experimental findings on atypical shell damage mode and extent. The influence of test fixture compliance is evaluated and briefly discussed.

Modulus development during reactive urethane foaming

During reactive urethane foaming a delicate balance involving bubble growth, phase separation, and network polymerization is established under adiabatic conditions. Little progress has been reported in the measurement of rheological changes for this relatively fast (3–5 min) and highly exothermic process. A flooded parallel plate fixture was designed and adapted to follow modulus build‐up in a Rheometrics System Four rheometer. The new geometry is able to accommodate the 20–40 fold volume change observed during foaming as well as to minimize interference by the skin on the foam surface. The influence of edge effects and fixture compliance was studied by testing different cup radii and gap heights with strain and frequency sweeps on a low viscosity polydimethylsiloxane and a shaving cream foam. The evolution of storage (G’) and loss (G‘) moduli during foaming was measured on a typical slabstock foam formulation at 2.0 and 4.2 g water per 100.0 g polyol. Four regions were identified during the foaming process: 1. Bubble nucleation, within the initial 30 s of reaction; 2. Liquid foam, a network of interacting bubbles leads to a solid‐like plateau in G’; 3. Phase separation which leads to rapid modulus rise and cell opening; and 4. Foamed elastomer, where the final (foam) modulus is reached.

Modulus Development During Reactive Urethane Foaming

During reactive urethane foaming a delicate balance involving bubble growth, phase separation, and network polymerization is established under adiabatic conditions. Little progress has been reported in the measurement of rheological changes for this relatively fast (3–5 min) and highly exothermic process. A flooded parallel plate fixture was designed and adapted to follow modulus build‐up in a Rheometrics System Four rheometer. The new geometry is able to accommodate the 20–40 fold volume change observed during foaming as well as to minimize interference by the skin on the foam surface. The influence of edge effects and fixture compliance was studied by testing different cup radii and gap heights with strain and frequency sweeps on a low viscosity polydimethylsiloxane and a shaving cream foam. The evolution of storage (G’) and loss (G‘) moduli during foaming was measured on a typical slabstock foam formulation at 2.0 and 4.2 g water per 100.0 g polyol. Four regions were identified during the foaming proce...