W. G. Knauss

One dimensional modelling of failure in laminated plates by delamination buckling

When low speed objects impact composite laminated plates delamination may result. Under inplane compression such delaminations may buckle and tend to enlarge the delaminated area which can lead to loss of global plate stability. This process is modelled here in a first attempt by a delaminating beam-column wherein the local delamination growth, stability and arrest are governed by a fracture mechanics-based energy release rate criterion.

Submicron deformation field measurements : Part 2. Improved digital image correlation

This is the second paper in a series of three devoted to the application of scanning tunneling microscopy (STM) to mechanics problems. In this paper, improvements to the digital image correlation method are outlined, a technique that compares digital images of a specimen surface before and after deformation to deduce its two-dimensional surface displacement field and strains. The necessity of using the framework of large deformation theory for accurately addressing rigid body rotations to reduce associated errors in the strain components is pointed out. In addition, the algorithm is extended to compute the three-dimensional surface displacement field from STM data; also, significant improvements are achieved in the rate as well as the robustness of the convergence. For (STM) topographs, the resolution yields 4.8 nm for the in-plane and 1.5 nm for the out-of-plane displacement components spanning an area of 10 μm×10μm.

An experimental investigation into dynamic fracture: III. On steady-state crack propagation and crack branching

This is the third in a series of four papers in which problems of dynamic crack propagation are examined experimentally in large, thin sheets of Homalite-100 such that crack growth in an unbounded plate is simulated. In the first paper crack initiation resulting from stress wave loading to the crack tip as well as crack arrest were reported. It was found that for increasing rates of loading in the microsecond range the stress intensity required for initiation rises markedly. Crack arrest occurs abruptly without any deceleration phase at a stress intensity lower than that which causes initiation under quasi-static loading.In the second paper we analyze the occurrence of micro cracks at the front of the running main crack which control the rate of crack growth. The micro cracks are recorded by real time photography. By the same means it is shown that these micro cracks grow and turn away smoothly from the direction of the main crack in the process of branching.In the present paper we report results on crack propagation and branching. It is found that crack propagation occurs at a constant velocity although the stress intensity factor changes markedly. Furthermore, the velocity is determined by the stress wave induced intensity factor at initiation. The terminal velocity in Homalite-100 was found to be about half the Rayleigh wave speed (0.45 Cr). These observations are analyzed in terms of a microcrack model alluded to in the second paper of this series. A mechanism for crack branching is proposed which considers branching to be a natural evolution from a “cloud” of microcracks that accompany and lead the main crack. These results are believed to apply to quasi-brittle materials other than Homalite-100 and the reasons for this belief are discussed briefly in the first paper of this series.In the final paper of the series the effect of stress waves impinging on the tip of a rapidly moving crack is examined. Waves affect the velocity and the direction of propagation as well as the process of crack branching.

Poisson's Ratio in Linear Viscoelasticity – A Critical Review

Poissons ratio is an elastic constant defined as the ratio of thelateral contraction to the elongation in the infinitesimal uniaxialextension of a homogeneous isotropic body. In a viscoelastic materialPoissons ratio is a function of time (or frequency) that depends on thetime regime chosen to elicit it. It is important as one of the materialfunctions that characterize bulk behavior.This paper develops the linear theory of the time- orfrequency-dependent Poissons ratio, and it reviews work on itsexperimental determination. The latter poses severe difficulties in viewof the high accuracy required. Thus, reliable information on theviscoelastic Poissons ratio is as yet rather scanty.The paper also reports on attempts to measure the Poissons ratioof a viscoelastic material as a function of temperature. Lateralcontraction in creep and at constant rate of extension receivesattention as well.

A new microtensile tester for the study of MEMS materials with the aid of atomic force microscopy

An apparatus has been designed and implemented to measure the elastic tensile properties (Youngs modulus and tensile strength) of surface micromachined polysilicon specimens. The tensile specimens are “dog-bone” shaped ending in a large “paddle” for convenient electrostatic or, in the improved apparatus, ultraviolet (UV) light curable adhesive gripping deposited with electrostatically controlled manipulation. The typical test section of the specimens is 400 μm long with 2 μm×50 μm cross section. The new device supports a nanomechanics method developed in our laboratory to acquire surface topologies of deforming specimens by means of Atomic Force Microscopy (AFM) to determine (fields of) strains via Digital Image Correlation (DIC). With this tool, high strength or non-linearly behaving materials can be tested under different environmental conditions by measuring the strains directly on the surface of the film with nanometer resolution.

NON-LINEAR VISCOELASTICITY BASED ON FREE VOLUME CONSIDERATION

Abstract Many advanced engineering problems suffer from inadequate solution because the appropriate constitutive behavior for the materials involved is not available. This is certainly true where polymers are concerned because in many situations involving failure analysis the non-linear viscoelastic material properties become important. In this paper a non-linear viscoelastic constitutive law is considered. It starts from the assumption that linear viscoelasticity is appropriate under infinitesimal strains and that the material description must revert to this case. The non-linearity of this development is derived from the stress dependent time response in the deformation process. The physical basis for the description derives from the observation that stress induced dilatation effects the mobility of molecular chains through changing the free volume in the polymer. Test data for polyvinyl acetate are compared with computations under conditions of relaxation and constant strain rate deformation. Excellent agreement is obtained between the proposed model and experiments. This agreement would indicate that the free volume model is definitely a possible way of describing non-linear viscoelastic behavior under small to moderate strains.

The mechanical strength of polysilicon films : Part 2. Size effects associated with elliptical and circular perforations

Abstract A systematic study of failure initiation in small-scale specimens has been performed to assess the effect of size scale on “failure properties” by drawing on the classical analysis of elliptically perforated specimens. Limitations imposed by photolithography restricted the minimum radii of curvature of the specimen perforations to one micron. By varying the radius of curvature and the size of the ellipses, the effects of domain size and stress concentration amplitude could be assessed separately to the point where the size of individual grains (∼0.3 μm ) becomes important. The measurements demonstrate a strong influence of the domain size under elevated stress on the “failure strength” of MEMS scale specimens, while the amplitude, or the variation, of the stress concentration factor is less significant. In agreement with probabilistic considerations of failure, the “local failure strength” at the root of a notch clearly increases as the radius of curvature becomes smaller. Accordingly, the statistical scatter also increases with decreasing size of the (super)stressed domain. When the notch radius becomes as small as 1 μm the failure stress increases on average by a factor of two relative to the tension values derived from unnotched specimens. This effect becomes moderate for larger radii of curvature, up to a radius of 8 μm (25 times the grain size), for which the failure stress at the notch tip closely approaches the value of the tensile strength for un-notched tensile configurations. We deduce that standard tests, performed on micron-sized, non-perforated, tension specimens, provide conservative strength values for design purposes. In addition, a Weibull analysis shows for surface-micromachined specimens a dependence of the strength on the specimen length, rather than the surface area or volume, which implies that the sidewall geometry, dimensions and surface conditions can dominate the failure process.

Mechanical measurements at the micron and nanometer scales

Abstract Experimentation at the micron level requires specific tools and methods. It will be illustrated how some of these tools have to be combined to achieve this goal. Because the determination of strains at the micron and nanoscales has been explored with the aid of probe microscopy, attention needs to be devoted to the limitations of digital image correlation. In this context it is illustrated how the results of the correlation method are affected by several process parameters, such as subset size, out-of-plane deformation, displacement gradients and scanning noise introduced in measurements. We also present measurements of material fracture on small, elliptically perforated (MEMS) specimens under tension via specially constructed equipment. Of particular interest is how the failure strength of polycrystalline silicon (grain size ∼0.3 μm) is influenced by the magnitude of the notch radius (1–8 μm) and the stress concentration factor (3–10). It is demonstrated that when the notch radius falls below 3 μm, the strength of the material is no longer governed by the critical stress criterion that controls failure initiation for larger radii (e.g. 8 μm or larger). In fact, the stress gradient plays a significant role in the failure process, which is explained in terms of the statistical spatial distribution of small flaws or cracks and the size of the zone at the notch tip under high stress. Failure stresses increase by a factor of two or more at a characteristic size of 1 μm.

A reconciliation of dynamic crack velocity and Rayleigh wave speed in isotropic brittle solids

Following earlier observations of multiple micro-crack formation accompanying crack propagation under dynamic conditions, the question regarding the discrepancy between the ‘theoretically anticipated’ maximal crack (Rayleigh wave) speed and those observed typically in amorphous, isotropic solids is examined experimentally. It is shown that if the production of these multiple micro-cracks ahead of the main fracture is suppressed by fabricating a material possessing a thin uniform region of vanishing intrinsic (molecular/atomic) material strength, the crack speed is materially increased to the point of approaching the Rayleigh wave speed. Moreover, it is also shown that the presence of small discreet flaws of sufficient spatial density similarly ‘weakens’ the material to produce fracture speeds comparable to the Rayleigh wave speed. One deduces, therefore, that for a single crack front the linearized theory of elastodynamics correctly predicts the dynamic crack propagation behavior of a solid with sufficiently low material strength.

Observation of damage growth in compressively loaded laminates

An experimental program to determine the phenomenological aspects of composite-panel failure under simultaneous compressive in-plane loading and low-velocity transverse impact [0-75 m/s (0-250 ft/s)] is described. High-speed photography coupled with the shadow-moiré technique is used to record the phenomenon of failure propagation. The information gained from these records, supplemented by plate sectioning and observation for interior damage, has provided information regarding the failure-propagation mechanism.The results show that the failure process can be divided roughly into two phases. In the first phase the plate is impacted, and the resulting response causes interlaminar separation. In the second phase the local damage spreads to the undamaged portion of the plate through a combination of laminae buckling and further delamination.