Creep Stress Distribution Research Articles

Modified state space method for bending creep and recovery behaviors of viscoelastic orthotropic laminated plate

A modified state space method (SSM) is proposed first to solve the analytical solution of viscoelastic orthotropic laminated (VOL) plate under time-varying load. This modification extends the applicability of traditional SSM from elastic materials to viscoelastic materials by resolving a limitation of the traditional SSM, where computing the exponential function of the state space matrix is infeasible. In the analytical model, the long-term stresses and displacements are established based on the orthotropic elasticity theory combined with the Boltzmann superposition. The convolution within the governing equation is resolved through Laplace transform. By using the proposed modified SSM, the general solution for each viscoelastic lamina is derived out, by separating the complex variable of Laplace transform out from the state space matrix. The analytical solution is ultimately derived using series expansion, transfer matrix method and inverse Laplace transform. The proposed model can provide long-term creep stress distribution in the VOL plate by creep deflection data from experiment. The comparison with existing results indicates the proposed solution exhibits greater accuracy than simplified solutions and higher efficiency compared to the finite element method. At last, the bending creep and recovery behaviors of the VOL plate are investigated in detail.

Pt–Al bond coat dependence on the creep stress distribution, deformation and fracture behaviour in a second generation Ni-based single crystal superalloy

An evaluation was conducted on the impact of a Pt–Al bond coat on the creep behaviours of a second-generation Ni-based single crystal superalloy at 750 °C/820 MPa, 850 °C/630 MPa, 1038 °C/137 MPa and 1100 °C/112 MPa, respectively. As revealed by the creep results, the creep behaviours of the coated superalloy were inferior to those of the bare superalloy to some extent under all testing conditions. The maximum deterioration in the strain-to-fracture and time-to-rupture was observed at 1100 °C/112 MPa (7.3%) and 750 °C/820 MPa (74.7 h), respectively. Following the creep test, deconvolution calculations were performed, which indicated that the creep stress for all core superalloys was as low as approximately 1.7–1.9% of the applied stress while the bond coat stress was 4.0–10.4% that at the minimum creep rate. Moreover, TEM analyses revealed that within the superalloy substrate adjacent to the bond coat, there were fewer stacking faults and an abundance of dislocation debris observed within γ′-Ni3Al at 750 °C/820 MPa. The misfit of the γ/γ′ phase was insignificant and the dislocation networks became irregular at 1100 °C/112 MPa. With an increase in temperature from 750 °C to 1100 °C, the fracture mechanism of both the substrate and bond-coat was found to shift from quasi-cleavage to micro-void coalescence. The quasi-cleavage cracks occurring within the bond coat increased the number of connections with creep cracks to cause spreading from the interior of the samples, thus resulting in premature failure at 750 °C/820 MPa and 850 °C/630 MPa. However, the degradation at 1038 °C/137 MPa and 1100 °C/112 MPa was ascribed to the increasing thickness of the inter-diffusion zone, as well as the volume of the blocky γ′-Ni3Al phase inside the bond coat and topologically close-packed phases in the superalloy near the bond coat.

Time-Dependent Electro–Magneto–Thermoelastic Stresses of a Poro-Piezo-Functionally Graded Material Hollow Sphere

In this paper, analytical solution for time-dependent electro–magneto–thermoelastic stresses of a hollow sphere made of a fluid-saturated functionally graded porous piezoelectric material (FGPPM) is presented. All material properties, except Poisson's ratio, vary through the radial direction of the FGPPM spherical structure according to a simple power-law. The general form of thermal, mechanical, and electric potential boundary conditions is considered on the internal and external surfaces of the sphere, and the sphere is under constant electrical and magnetic fields. Stress–strain and strain–displacement relations are used to obtain stress–displacement equations, and then by putting stress–displacement equations in the equilibrium equation, Navier equation is acquired. The homogenous differential heat conduction equation is solved. The nonhomogenous differential Navier equation is solved for two cases. At first, creep strains are ignored and the initial electro–magneto–thermoelastic stresses are obtained. Then considering creep strains singly, the creep stress rates are obtained. Finally, time-dependent creep stress distributions at any time ti are attained.

Creep analysis for a functionally graded cylinder subjected to internal and external pressure

In this paper the creep behaviour of a functionally graded cylinder is considered under both internal and external pressures. When the properties of the graded material are axisymmetric and dependent on the radial coordinate, an asymptotic solution can be derived on the basis of a Taylor expansion series. The approximate solutions calculated from different higher-order terms are compared with the results of finite element (FE) analysis using ABAQUS software. It is shown that, although the use of higher-order terms may help to obtain a more accurate result for the time-dependent behaviour of the cylinder, a fifth-order form has been sufficiently accurate to calculate the creep stress distribution with satisfactory approximation.

An analytical and computational study of crack initiation under transient creep conditions

An analytical method has been developed to predict creep crack initiation (CCI), based on the accumulation of a critical level of damage at a critical distance. The method accounts for the re-distribution of stress from the elastic or elastic–plastic field, experienced on initial loading, to a steady state creep stress distribution, via a transient creep region. The method has been applied to predict CCI times in a fracture specimen of type 316H stainless steel at 550 °C. The failure model has been also been implemented into a finite element (FE) framework. Reasonable and conservative predictions of CCI time can be obtained from the analytical solution relative to FE solutions. Conservative predictions of experimental CCI times are obtained when stress redistribution is taking into account. However, CCI times predicted from a steady state creep model are found to be non-conservative.

Finite element analysis of notched bar skeletal point stresses and dimension changes due to creep

ABSTRACTIn this investigation, finite element calculations have been performed to obtain the creep stress distributions generated in circumferentially notched bar test‐pieces. They have also been made to determine the relation between axial extension and notch throat diameter changes. It has been found that an approximate skeletal point can be identified where the stress state is insensitive to the power law stress dependence of creep. Consistent trends in skeletal point stress ratios to those given in an existing Code of Practice for notch bar creep testing have been obtained. Nevertheless updated values, particularly for sharp notches, are proposed and these have now been inserted into a new version of the Code of Practice. In contrast, the link between extension and notch throat diameter changes has been found to depend on the creep stress index as well as the notch geometry. It is anticipated that the analysis can be used to establish the multi‐axial creep stress deformation and rupture behaviour of materials.

Effect of Stress States on Creep Fracture Modes of an Austenitic Steel with High Ductility.

Tensile creep rupture tests using smooth specimens and circumferential U-notched specimens having 4 kinds of notch root radius, and torsional creep rupture tests using smooth and circumferential 60° V-notched specimens of SUS310S austenitic steel with high ductility and high metallographical stability, were conducted at 700°C. In tensile creep rupture tests, it was found that as turning into lower stress level the creep fracture mode of smooth specimens changed from ductile transgranular fracture to brittle intergranular fracture. And irrespective of applied stress and notch geometry, the creep fracture mode of all notched specimens showed brittle intergranular fracture mixed with ductile transgranular fracture. While in torsional creep rupture tests, all smooth and notched specimens in the present test range exhibited a ductile fracture of shear type. These creep fracture modes were discussed on the basis of stress states and steady-state creep stress distributions in notch cross sections calculated by finite element method. The results suggested that mean stress promotes the intergranular creep fracture strongly, and that the equivalent stress promotes the nucleation of intergranular cavities but contributes less to their growth.

Determining High Temperature Properties of Weld Materials.

Welds form an integral part of most power and chemical plant syructures. At elevated temperature, the service life of these structures are often governed by the creep behaviour of welds. Efforts have been made to understand creep stress distributions in and deformation behaviour of welds and to predict the failure life. In this context, the determination of the high temperature properties of welds is essential. However, due to the complex nature of the material inhomogeneity in the weld regions, accurate determination of material properties of welds is not a straight forward task. This paper describes some aspects related to the determination of high temperature material properties of welds. Experimental creep testing methods involved and the procedures for generating the material constants in creep and damage constitutive equations for the parent, HAZ and weld material zones of welds are introduced, Practical applications of these techniques are discussed and the results obtained from typical high temperature CrMoV welds in main steam pipe lines are presented.

Creep Relaxation in Multilayer Wrapped Vessels

One of the common methods of construction of vessels for high to ultra-high pressure applications is the wrapping technique. In this method, relatively thin plates (normally in the range of 6 mm) are rolled to proper curvature, wrapped around the core or the preceding layers and then welded. In this fashion, a prestress is gradually built in the cylinder wall which would compensate and moderate the extreme stresses due to internal pressure. Relying on such prestress, however, should be done only with careful consideration of stress relaxation that will take place while the vessel is in service, especially in high temperature services. In this paper, the initial stresses due to wrapping are obtained. These stresses are due to shrinkage of the weld as well as the plate affected by the heat of welding. The power function stress-creep strain rate is employed to predict the relaxation of interface pressure between any two adjacent layers. The creep stress distribution based on relaxing interface pressures are given as a function of time. In such vessels, in order to maintain the same safety factor as existed when the vessel was constructed, the internal pressure must be decreased with time. A relationship between the internal pressure and time, based on a constant safety factor, is obtained. Alternately, for the case of internal pressure being kept at the same level, a relationship is obtained that would give the decreasing safety factor or the vessel as a function of time.

Influence of constraint on creep stress distribution in notched bars

Stresses and strains occuring during creep were determined for circumferentially notched round bars having several specimen notch geometries representing different degrees of constraint. The specimen geometries and the material data used in the calculations were those pertaining to a parallel experimental investigation. It was found that, for the wide notch specimens, the notch to net-section radius ratio has a greater influence on the degree of constraint than the notch depth ratio. For the thin slit specimen, the small slit tip radius to net section radius ratio caused a big difference in stress distribution from that for the wide notch specimen of the same net-to-gross radius ratio. Global and local events were distinguished by the change of notch sharpness: for the relatively wide notch, creep was mainly a global process, whereas for the sharp slit, the creep process remained in a very local region near the slit tip. Various indicators for the degree of constraint are discussed, of which the triaxiality factor I1/σ seemed to be the most useful.