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Linearly viscoelastic strip with slowly propagating central crack, calculating stress intensity factor and crack opening size
The VISCEL program is a general purpose computer program developed for equilibrium analysis of linear viscoelastic structures. The program is written in FORTRAN 5 language to operate on the Univac 1108 computer under the EXEC 8 operating system. The program, an extension of the linear equilibrium problem solver ELAS, is an updated and extended version of its earlier form written for the IBM 7094 computer. Finite element matrix displacement approach coupled with the synchronized material property concept, utilizing incremental time steps, was adopted for the solution presented. The step-by-step procedure involves solution of recursive equations in the time domain, which takes into account the memory of material properties. Incremental and accumulative displacements and stresses are obtained at the end of each time step. In order to minimize the extent of computations resulting from accumulative effects of material memory, the program provides an option which enables the employment of constant time steps in the logarithmic scale. Program documentation is presented.
This program, an extension of the linear equilibrium problem solver ELAS, is an updated and extended version of its earlier form (written in FORTRAN 2 for the IBM 7094 computer). A synchronized material property concept utilizing incremental time steps and the finite element matrix displacement approach has been adopted for the current analysis. A special option enables employment of constant time steps in the logarithmic scale, thereby reducing computational efforts resulting from accumulative material memory effects. A wide variety of structures with elastic or viscoelastic material properties can be analyzed by VISCEL. The program is written in FORTRAN 5 language for the Univac 1108 computer operating under the EXEC 8 system. Dynamic storage allocation is automatically effected by the program, and the user may request up to 195K core memory in a 260K Univac 1108/EXEC 8 machine. The physical program VISCEL, consisting of about 7200 instructions, has four distinct links (segments), and the compiled program occupies a maximum of about 11700 words decimal of core storage.
Previously a method was developed for predicting the viscoelastic response of polymers undergoing scission reactions. These results are now extended to include crosslinking reactions. As for scission, at any given time the character of the network chains is determined by the instantaneous crosslink density. For scission all chains were assumed to carry the same stress; for crosslinking, however, the stress is distributed between the 'new' and 'old' chains. Equations for calculating the creep response of a system which experiences a step increase in crosslink density are derived.
The response of an infinite Bernoulli-Euler plate placed on the surface of a randomly vibrating viscoelastic half-space is calculated, allowing for the presence of shear stresses between the plate and the half-space. The shear stresses arise from the condition that the relative motion between the plate and the half-space vanishes at the interface. The three components of displacement of the free surface of the half-space before the plate is added are assumed to be stationary homogeneous random functions of position and time. From the wavenumber-frequency spectra of these displacements the frequency spectra of the three components of displacement of the plate half-space interface are calculated. As an example, the frequency spectrum of the vertical interface displacement is calculated for two assumed forms of the wavenumber spectra of the free-surface displacements.
Technique computes stresses resulting from axisymmetric transient thermal loading in circular solid-propellant grain section with circular ports. Propellant is assumed to be linear, thermal rheologically simple, viscoelastic material; material properties are represented by exponential series in time.
Research projects concerned with developing a theory of fracture of materials are discussed. The effects of the geometry of the structure and the loads acting on the structure as they influence the failure process are analyzed. The effects of the viscoelastic deformation characteristics of the bulk elastomer on failure behavior are examined. Additional material parameters which control the fracture process are identified.
A method is presented of determining the mean square transversal deflection of an isotropic and homogeneous linear viscoelastic beam having a certain number of lengthwise distributed lumped masses. It is assumed that the beam is acted upon by a stationary random process uniformly distributed along the beam. The method is useful in vibration level control by means of additional lumped masses.
A kinetic model for characterizing the shear stress or shear strain rate of thixotropic materials is developed and combined with Oldroyd's viscoelastic model (1953) modified in this paper in order to predict the first normal stress difference. In order to test the method, transient and steady state data have been obtained with a Weissenberg rheogoniometer used to measure the constant stress and constant shear rate of a solution of polymethyl methacrylate in diethylphthalate. A computer was used to facilitate data acquisition.
Subcritical crack growth in a linear viscoelastic material subjected to cyclic loading is investigated starting with the thermodynamic power balance. Physically, it is supposed that the subcritical slow crack growth is due to local weakening of the material in the neighborhood of the crack tip. Under fatigue loading it is assumed that all energy dissipation goes into heat and that this heat build-up is the dominant irreversible process governing crack growth. The cycle averaged temperature distribution around the crack tip is obtained from local application of the first law of thermodynamics (i.e., conservation of energy). The analysis leads to the solution of a nonlinear integro-differential equation for crack length as a function of time which is coupled with the local energy equation. A regular perturbation technique is used to obtain an analytical solution which compares very well with experimental results.
The equilibrium stability criterion for diffuse interfaces in a two-component solution with a miscibility gap requires that the interdiffusion flux vanish. If the system is continuously deformed, convective fluxes disrupt the equilibrium in the interface regions and induce a counter diffusive flux, which is dissipative and contributes to the apparent viscosity of the mixture. Chemical free energy is recoverably stored, causing viscoelastic phenomena. Both effects are significant.
Synthetic polymer models of several degrees of softness were subjected to standard creep tests to determine their viscoelastic characteristics. The automatic measuring apparatus and the theory of measurement used in modeling the human recognition of the softness factor are described.
An analytical study on low frequency noise transmission into rectangular enclosures by viscoelastic sandwich panels is presented. Soft compressible cores with dilatational modes and hard incompressible cores with dilatational modes neglected are considered as limiting cases of core stiffness. It is reported that these panels can effect significant noise reduction.
The time-temperature response of the principal compliances of a unidirectional graphite/epoxy composite was determined. It is shown that two components of the compliance matrix are time and temperature independent and that the compliance matrix is symmetric for the viscoelastic composite. The time-temperature superposition principle is used to determine shift factors which are independent of fiber orientation, for fiber angles that vary from 10 D to 90 D with respect to the load direction.
Necessary fundamentals relative to composite materials and viscoelasticity are reviewed. The accelerated characterization techniques of time temperature superposition and time temperature stress superposition are described. An experimental procedure for applying the latter to composites is given along with results obtained on a particular T300/934 graphite/epoxy. The accelerated characterization predictions are found in good agreement with actual long term tests. A postcuring phenomenon is discussed that necessitates thermal conditioning of the specimen prior to testing. A closely related phenomenon of physical aging is described as well as the effect of each on the glass transition temperature and strength. Creep rupture results are provided for a variety of geometries and temperatures for T300/934 graphite/epoxy. The results are found to compare reasonably with a modified kinetic rate theory.
A method for the synthesis and manufacturing of elastomeric compositions and articles containing quaternary nitrogen centers and condensation residues along the polymeric backbone of the centers is presented. Linear and cross-linked straight chain and block polymers having a wide damping temperature range were synthesized. Formulae for the viscoelastic cationic polymers are presented.
A testing program was conducted to determine the time-temperature response of the principal compliances of a unidirectional graphite/epoxy composite. It was shown that the two components of the compliance matrix are time and temperature independent. In addition, the compliance matrix is symmetric for the viscoelastic composite. The time-temperature superposition principle is used to determine shift factors. It was shown that the shift factors are independent of fiber orientation for fiber angles that vary from 10 to 90 deg with respect to the load direction.
The propagation of ultrasonic waves guided along a viscoelastic layer which separates two dissimilar elastic solid half spaces is described. For the limiting cases of rigid and soft bonding by a layer thin compared to acoustic wavelength, Stoneley and independent Rayleigh wave characteristic equations, respectively, result. For combinations of layer rigidity and wave length that correspond to guided wave propagation, external cyclic loading of the layer produces mechanical hysteresis and a resulting dynamic change in bond properties. Measurements of velocity hysteresis in an aluminum polymer adhesive aluminum system are described.