Peter Gudmundson

Eigenfrequency changes of structures due to cracks, notches or other geometrical changes

A first order perturbation method is presented which predicts the changes in resonance frequencies of a structure resulting from cracks, notches or other geometrical changes. The eigenfrequency changes due to a crack are shown to be dependent on the strain energy of a static solution which is easily obtainable for small cracks and other small cut-outs. The method has been tested for three different cases, and the predicted results correlate very closely to experimental and numerical results.

The dynamic behaviour of slender structures with cross-sectional cracks

A dynamic model for beams with cross-sectional cracks is discussed. It is shown that a crack can be represented by a consistent, static flexibility matrix. Two different methods for the determination of the flexibility matrix are discussed. If the static stress intensity factors are known, the flexibility matrix can be determined from an integration of these stress intensity factors. Alternatively, static finite element calculations can be used for the determination of the flexibility matrix. Both methods are demonstrated in the present paper. The mathematical model was applied to an edge-cracked cantilevered beam and the eigenfrequencies were determined for different crack lengths and crack positions. These results were compared to experimentally obtained eigenfrequencies. In the experiments, the cracks were modelled by sawing cuts. The theoretical results were, for all crack lengths, in excellent agreement with the experimental data. The dynamic stress intensity factor for a longitudinally vibrating, centrally cracked bar was determined as well. The results compared very well with dynamic finite element calculations. The crack closure effect was experimentally investigated for an edge-cracked beam with a fatigue crack. It was found that the eigenfrequencies decreased, as functions of crack length, at a much slower rate than in the case of an open crack.

An analytic model for thermoelastic properties of composite laminates containing transverse matrix cracks

An analytical model for the prediction of the thermoelastic properties of composite laminates containing matrix cracks is presented. In particular, transverse matrix cracks with their crack surfaces parallel to the fibre direction and perpendicular to the laminate plane are treated. Two- and three-dimensional laminates of arbitrary layup configurations are covered by the model. The presented expressions for stiffnesses, thermal expansion coefficients, strain contributions from release of residual stresses and local average ply stresses and strains do solely contain known ply property data and matrix crack densities. The key to the model is the judicious use of a known analytical solution for a row of cracks in an infinite isotropic medium. The model has been verified against numerically determined stiffnesses, thermal expansion coefficients and local average ply stresses for matrix cracked angle-ply and cross-ply laminates. Comparisons to experimental data for cross-ply laminates are also presented. It is shown that the present model to a very good accuracy can predict thermoelastic properties of matrix cracked composite laminates at varying matrix crack densities and layup configurations.

First order analysis of stiffness reduction due to matrix cracking

In this paper the reduction in effective elastic constants of composite lami nates due to matrix cracking is considered. A general easily applicable theory valid for two- and three-dimensional analysis of thin as well as thick laminates is presented. The theory is based on the change of elastic energy in a laminate at the appearance of a matrix crack in one layer. This information combined with a dilute approximation , i.e., different matrix cracks are considered not to interact with each other, is utilized to estimate the re duction of elastic constants for a certain crack density. The theory is asymptotically exact for nk « 1, where nk is the number of cracks per unit thickness of the cracked ply and a correct value of the slope of the stiffness reduction crack density curve is obtained at nk = 0.

Three-dimensional periodic Voronoi grain models and micromechanical FE-simulations of a two-phase steel

Abstract A three-dimensional model is proposed for modeling of microstructures. The model is based on the finite element method with periodic boundary conditions. The Voronoi algorithm is used to generate the geometrical model, which has a periodic grain structure that follows the original boundaries of the Voronoi cells. As an application, the model is used to model a two-phase ferrite/pearlite steel. It is shown that periodic cells with only five grains generate representative stress–strain curves.

The usage of standard finite element codes for computation of dispersion relations in materials with periodic microstructure

A method with which standard finite element programs can be used to compute dispersion relations in periodic composites is proposed. The method is applied to two composite microstructures: a two-phase laminate and a fiber composite. The dispersion relations computed for the laminate are compared with a known analytical solution and the agreement is very good. The dispersion relations computed for the fibrous composite are compared with an existing approximate model and experimental results from the literature. The agreement between the approximate model, the experiments, and the computations is very good in the wave guide case and satisfactory for the wave reflect case.

Effects of a composite-like stress state on the fracture of epoxies

The strain to failure of a transversely loaded composite is much lower than for the pure matrix in uniaxial tension. Several studies of composites suggest the triaxial matrix stress state as one of the explanations. In order to investigate this experimentally, a triaxial tensile test previously used for rubbers (the poker-chip test) was successfully applied to four epoxies in the glassy state. The chosen specimen geometry mimicked the most severe stress state in the matrix as determined by finite element analysis of a transversely loaded glass-fiber/epoxy composite. The poker-chip strains to failure in the primary loading direction were 0.5-0.8%, whereas uniaxial strains to failure were 1.8-7%. The triaxial stress state in composite matrices may therefore by itself be a sufficient explanation for low values of transverse composite strains to failure.

Thermoelastic properties in combined bending and extension of thin composite laminates with transverse matrix cracks

Approximate analytic expressions for the thermoelastic properties in combined bending and extension of composite laminates containing transverse matrix cracks are derived. The model covers two-dimensional laminates of arbitrary lay-up sequences. The derived expressions for the compliances and thermal expansion coefficients merely contain ply property data and crack distributions. In order to check the accuracy and reliability of the presented analytic method, some sample cracked geometries were examined by use of the finite element method. A good agreement was found between the numerically and analytically obtained results for all cases under consideration.

Matrix crack initiation and progression in composite laminates subjected to bending and extension

An experimental investigation of matrix crack initiation and progression in glass/epoxy laminates of different stacking sequences is presented. The laminates have been loaded in extension and bending, and the degree of damage as function of the load has been recorded. The changes in certain elastic properties caused by the damage were also measured, and are compared to results from a previously developed approximate analytic model. An energy release rate resistance curve is adopted in an attempt to describe the initiation and progression of matrix cracks in the laminates. The amount of cracking is also viewed in relation to the strain transverse to the fibres in the ply under consideration, and the ply stresses at the onset of cracking are calculated. The different damage evolution criteria are compared to the experimental results, and their validity and reliability are discussed. By use of the ply strain transverse to the fibres as a critical parameter for damage evolution, the load-deformation curves of the tested laminates are simulated taking damage progression into account.

Broad-band transient recording and characterization of acoustic emission events in composite laminates

Acoustic emission (AE) transients due to different kinds of microdamage, such as matrix cracking, fiber breakage and local delaminations, have been recorded in glass/epoxy composite laminates. Different stacking sequences, [0 degrees, 90(2)degrees](S), [90(2)degrees, 0 degrees](S), [+45 degrees, -45 degrees](S) and [0(4)degrees], were used in order to trigger different crack mechanisms during tensile testing. The AE transients were recorded as functions of time by the use of broad-band AE transducers. In the experiments, it was observed that different types of cracks generated acoustic emission signals varying in amplitude, duration time and frequency content. It was also seen that the same type of crack produced signals with different characteristics depending on the layer in which the crack appeared and its orientation compared to the location of the transducer. The majority of signals from the tests could be divided into a few main groups. Typical signals and characteristics representing these groups are presented in the paper. The observations show that there is a potential in future development of quantitative methods for identification of damage development in composite laminates.