Law of nonlinear flow in saturated clays and radial consolidation

It was derived that micro-scale amount level of average pore radius of clay changed from 0.01 to 0.1 micron by an equivalent concept of flow in porous media. There is good agreement between the derived results and test ones. Results of experiments show that flow in micro-scale pore of saturated clays follows law of nonlinear flow. Theoretical analyses demonstrate that an interaction of solid-liquid interfaces varies inversely with permeability or porous radius. The interaction is an important reason why nonlinear flow in saturated clays occurs. An exact mathematical model was presented for nonlinear flow in micro-scale pore of saturated clays. Dimension and physical meanings of parameters of it are definite. A new law of nonlinear flow in saturated clays was established. It can describe characteristics of flow curve of the whole process of the nonlinear flow from low hydraulic gradient to high one. Darcy law is a special case of the new law. A math- ematical model was presented for consolidation of nonlinear flow in radius direction in saturated clays with constant rate based on the new law of nonlinear flow. Equations of average mass conservation and moving boundary, and formula of excess pore pressure distribution and average degree of consolidation for nonlinear flow in saturated clay were derived by using an idea of viscous boundary layer, a method of steady state in stead of transient state and a method of integral of an equation. Laws of excess pore pressure distribution and changes of average degree of consolidation with time were obtained. Re- sults show that velocity of moving boundary decreases because of the nonlinear flow in saturated clay. The results can provide geology engineering and geotechnical engineering of saturated clay with new scientific bases. Calculations of average degree of consolidation of the Darcy flow are a special case of that of the nonlinear flow.

A Generalized Non-Linear Flow Law Based on Modified Zerilli-Armstrong Model and Its Implementation into Abaqus/Explicit FEM Code

Non-linear numerical modeling, widely used in research and development to understand many complex processes such as forming or machining, does not guarantee the success of a study to be performed. Indeed, the numerical simulation uses finite element codes where the models already integrated are not based on shapes adjustable to any type of study. In this study, a new form of non-linear constitutive flow law based on the Modified Zerilli-Armstrong model, which can answer the above problem, has been developed to apply it to the numerical simulation of two different tests (a quasi-static compression test, the necking of a circular bar). This flow law is based on the modified Zerilli-Armstrong model, which, together with the new modified Johnson-Cook model, has been compared to appreciate the relevance of the proposal. For that, an implementation of this new law via the VUHARD subroutine into the Abaqus/Explicit finite element code was made to model the two tests. The comparison of the results obtained (from identification) by our proposed law with those obtained using the NMJC shows that this new law better approaches the experiments than the other one. This is also shown through the numerical results using the Abaqus software. It can be said that this way of formulating a flow law allows highlighting the great performance of the proposed approach. Although this law has been only used for quasi-static tests, we can say that it can also be used in dynamic tests.

Mathematical Model of a Hyperbolic Hydraulic Fracture with Tortuosity

The aim of the research is to study the propagation of a hydraulic fracture with tortuosity due to contact areas between touching asperities on opposite crack walls. The tortuous fracture is replaced by a model symmetric partially open fracture with a hyperbolic crack law and a modified Reynolds flow law. The normal stress at the crack walls is assumed to be proportional to the half-width of the model fracture. The Lie point symmetry of the nonlinear diffusion equation for the fracture half-width is derived and the general form of the group invariant solution is obtained. It was found that the fluid flux at the fracture entry cannot be prescribed arbitrarily, because it is determined by the group invariant solution and that the exponent n in the modified Reynolds flow power law must lie in the range 2 < n < 5. The boundary value problem is solved numerically using a backward shooting method from the fracture tip, offset by 0 < δ ≪ 1 to avoid singularities, to the fracture entry. The numerical results showed that the tortuosity and the pressure due to the contact regions both have the effect of increasing the fracture length. The spatial gradient of the half-width was found to be singular at the fracture tip for 3 < n < 5, to be finite for the Reynolds flow law n = 3 and to be zero for 2 < n < 3. The thin fluid film approximation breaks down at the fracture tip for 3 < n < 5 while it remains valid for increasingly tortuous fractures with 2 < n < 3. The effect of the touching asperities is to decrease the width averaged fluid velocity. An approximate analytical solution for the half-width, which was found to agree well with the numerical solution, is derived by making the approximation that the width averaged fluid velocity increases linearly with distance along the fracture.

Unsteady Rotative Flow of Non-Newtonian Fluid in an Annular Pipe

This paper .Studies power law no-Newtonian fluid rotative flow. in an annularpipe. The governing equation is nonlinear one, we linearized the governing equationby assuming that partial factor is at state. With Laplace transform we obtain ananalytical solution of the problem In the paper several groups of curves are given.these curves reflect the temporal change law and. spatial distribution of fluid velocity.In addition.we study the effection of power law index on the flow field the resultindicates that when the power law index n < l. the flow velocity is highly sensitive tothe index. and this fact is importanl in related engineering decisions.

Radially loading rotary extrusion for manufacturing large-size conical cylinders with inner transverse high ribs

The Large-size Conical Cylinders with Inner Transverse High Ribs(LCCWITHR) can reduce the weight of the parts while maintaining high rigidity and strength. Radially Loading Rotary Extrusion(RLRE) forming technology can achieve integral forming of LCCWITHR through the synergy of radial and rotary movements of dies. The flow law of the material during the forming process is the key to forming large-size inner ribs. At present, there is no unified understanding of the metal flow law of RLRE forming technology. An analytical expression was derived to predict the Radial Direction(RD) deformation loads. The FE simulation and process experiment were carried out to investigate the effects of the inclination angle, thickness factor and transition arc radius of the split top dies on the spacing of the metal diversion plane, the metal flow velocity of the rib area and the final radius of the inner rib. The influence of the split top dies loading distance and the bottom die rotation angle of each pass on the inner radius of the inner rib was verified. And the optimal combination of dies shape parameters and loading paths which can make the metal flow orderly was obtained: the inclination angle is 140°, the thickness factor is 3.64, the transition arc radius is 16 mm;the top dies loading distance is 15 mm, the bottom die rotation angle is 45°.The FE simulation results have been found to be in close agreement with physics experiment.The research results reveal the metal flow law of rib growth in the RLRE of LCCWITHR, which lays a theoretical foundation for subsequent thorough research and process optimization.

Dislocation Creep Accommodated by Grain Boundary Sliding in Dunite

To investigate the role of grain boundary sliding during dislocation creep of dunite, a series of deformation experiments were carried out under anhydrous conditions on fine-grained （-15 μm） samples synthesized from powdered San Carlos olivine and powdered San Carlos olivine＋1.5 vol.% MORB. Triaxial compressive creep tests were conducted at a temperature of 1 473 K and confining pressures of 200 and 400 MPa using a high-resolution, gas-medium deformation apparatus. Each sample was deformed at several levels of differential stress between 100 and 250 MPa to yield strain rates in the range of 10^-6 to 10^-4 s^-1. Under these conditions, the dominant creep mechanism involves the motion of dislocations, largely on the easy slip system （010）[100], accommodated by grain boundary sliding （gbs）. This grain size-sensitive creep regime is characterized by a stress exponent of n=3.4±0.2 and a grain size exponent of p=2.0±0.2. The activation volume for this gbs-accommodated dislocation creep regime is V＊=（26±3）×10^-6 m2·mol^-1. Comparison of our flow law for gbs-accommodated dislocation creep with those for diffusion creep and for dislocation creep reveals that the present flow law is important for the flow of mantle rocks with grain sizes of 〈100μm at differential stresses 〉20 MPa. Hence, gbs-accommodated dislocation creep is likely to be an important deformation mechanism in deep-rooted, highly localized shear zones in the lithospheric upper mantle.