Effect of three-dimensional deformation on the limit load of highly weld strength undermatched specimens under tension

2008 ◽  
Vol 222 (2) ◽  
pp. 107-115 ◽  
Author(s):  
S Alexandrov ◽  
M Kocak
Keyword(s):  
Upper Bound ◽  
Metal Forming ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Limit Load ◽  
Weld Strength ◽  
Structural Applications ◽  
Analytical Formulae ◽  
Current Article ◽  
Assessment Procedures

In the case of welded structures with cracks, a number of parameters, such as those with units of length, makes it difficult to present the results of numerical solutions in a form convenient for direct engineering applications, such as flaw assessment procedures. For centre-cracked components under tension, it is shown in the current article that an effect of crack length on the limit load can be taken into account by means of an upper bound limit load for the corresponding structure with no crack without any additional numerical treatment. Using this result, it is sufficient to find an upper bound limit load for the structure with no crack and then to apply the analytical formulae for finding the corresponding limit load for the structure of interest. Welding of some aluminium alloys for structural applications usually leads to a significantly lower strength (undermatched) weld joint. The approach proposed is used to demonstrate an effect of three-dimensional deformation on an upper bound limit load for such highly strength undermatched centre-cracked welded specimens under tension. This result can also be used in metal-forming applications where upper bound solutions are more useful than lower bound solutions.

A Simplified Kinematic Method for 3D Limit Analysis

2016 ◽  
Vol 846 ◽  
pp. 342-347 ◽  
Author(s):  
J.P. Hambleton ◽  
Scott William Sloan
Keyword(s):  
Upper Bound ◽  
Limit Analysis ◽  
Three Dimensional ◽  
Yield Condition ◽  
Limit Load ◽  
Computational Techniques ◽  
Simple Formulation ◽  
Planar Velocity ◽  
Collapse Mechanisms ◽  
Second Order Cone

The kinematic (upper bound) method of limit analysis is a powerful technique for evaluating rigorous bounds on limit loads that are often very close to the true limit load. While generalized computational techniques for two-dimensional (e.g., plane strain) problems are well established, methods applicable to three-dimensional problems are relatively underdeveloped and underutilized, due in large part to the cumbersome nature of the calculations for analytical solutions and the large computation times required for numerical approaches. This paper proposes a simple formulation for three-dimensional limit analysis that considers material obeying the Mohr-Coulomb yield condition and collapse mechanisms consisting of sliding rigid blocks separated by planar velocity discontinuities. A key advantage of the approach is its reliance on a minimal number of unknowns, can dramatically reduce processing time. The paper focuses specifically on tetrahedral blocks, although extension to alternative geometries is straightforward. For an arbitrary but fixed arrangement of blocks, the procedure for computing the unknown block velocities that yield the least upper bound is expressed as a second-order cone programming problem that can be easily solved using widely available optimization codes. The paper concludes with a simple example and remarks regarding extensions of the work.

Kinetic and Dynamic Effects on the Upper-Bound Loads in Metal-Forming Processes

1976 ◽  
Vol 43 (2) ◽  
pp. 314-318 ◽  
Author(s):  
Jehuda Tirosh ◽  
Shiro Kobayashi
Keyword(s):  
Upper Bound ◽  
Metal Forming ◽  
High Speed ◽  
Limit Load ◽  
Time Rate ◽  
Dynamic Head ◽  
Rate Effects ◽  
Machine Speed ◽  
Dependent Processes

The regular upper-bound approach in metal-forming processes is extended to time-dependent processes. The ultimate goal is to estimate, in an approximate manner, time rate effects such as machine speed and material inertia, on the forming load of time independent materials. The admissible velocity field with associated jumps is used to generate an acceleration flow field and associated flow resistance. Two fundamental nondimensional numbers emerge from the analysis for all processes considered. One is related to the speed at which the deforming load is applied, ρu02/σ0 (called the “kinetic head”) and the second is related to the acceleration of the deforming tool and its contact area with the flowing metal ρu˙0R/σ0 (called the “dynamic head”). The uniqueness of each specific process is characterized by appropriate functions representing the unsteady (or steady) pertinent geometry of the product and multiplying the foregoing numbers. The resulting expressions appear to be dominant only at relatively high speed and/or impact operations, and thus amplify the role of the time rate on the limit load. Three typical processes (forging, extrusion, and piercing) exemplify the approach with some experimental evidence.

Effect of Plastic Anisotropy on the Predictive Capacity of Flaw Assessment Procedures

2010 ◽  
Vol 638-642 ◽  
pp. 3821-3826 ◽  
Author(s):  
Sergei Alexandrov
Keyword(s):  
Yield Criterion ◽  
Input Parameter ◽  
Plastic Anisotropy ◽  
Three Dimensional ◽  
Base Material ◽  
Limit Load ◽  
Orthotropic Materials ◽  
Predictive Capacity ◽  
Essential Input ◽  
Assessment Procedures

The limit load is an essential input parameter of flaw assessment procedures. The present paper deals with an effect of plastic anisotropy on its value. An upper bound solution for three-dimensional deformation of a highly under-matched welded specimen subject to tension is proposed. The base material is assumed to be rigid, and the weld material obeys Hill’s quadratic yield criterion for orthotropic materials. It is demonstrated that it is crucial to account for both plastic anisotropy and three dimensionality of deformation in limit load calculations for flaw assessment procedures.

Optimising Fracture Assessment of Welded Structures Using BS 7910, R6 and FEA

2019 ◽  
Author(s):  
Isabel Hadley ◽  
Tyler London
Keyword(s):  
Residual Stress ◽  
Assessment Methods ◽  
Welding Residual Stress ◽  
Weld Strength ◽  
Materials Testing ◽  
Welded Structures ◽  
Analytical Formulae ◽  
Fracture Assessment ◽  
Crack Tip Constraint ◽  
Assessment Procedures

Abstract The fracture clauses of BS 7910 and R6 present a hierarchy of assessment methods. Depending on the data available, the user may adopt the simplest approach (Option 1), or the higher Options (2 & 3), allowing increasing accuracy and decreasing conservatism. Additional assessment procedures are available via the Annexes of BS 7910 and via Chapter III of R6, which address the inclusion of welding residual stress, crack tip constraint, weld strength mismatch and warm prestress. This paper illustrates the application of both basic and advanced fracture assessment procedures to a set of welded wide plate test data. The tests featured extensive materials testing, along with detailed characterisation of welding residual stress both in the as-welded condition and after a warm prestress treatment. The study shows how the accuracy of the assessment increases as the more advanced assessment methods are employed. A tailored assessment of the uniaxial tests using elastic-plastic FEA was also carried out, allowing a comparison between the analytical formulae given in BS 7910/R6, numerical analysis and experimental results.

On the Solution of Three-Dimensional Metal-Forming Processes

1977 ◽  
Vol 99 (3) ◽  
pp. 624-629 ◽  
Author(s):  
V. Nagpal
Keyword(s):  
Upper Bound ◽  
Metal Forming ◽  
Three Dimensional ◽  
Velocity Fields ◽  
Rectangular Shape ◽  
Admissible Velocity ◽  
Die Forging ◽  
Stream Functions ◽  
Open Die Forging

The use of “dual-stream functions” in analyzing some three-dimensional metal-forming processes is demonstrated in this paper. The problems discussed are open-die forging of blocks, rolling of a rectangular bar with spread, piercing by elliptic and rectangular punches, and extrusion of a rectangular shape. For these forming processes, kinematically admissible velocity fields are selected using characteristics of the two stream functions. Approximate upper-bound solutions of the forming processes can be obtained from the proposed velocity fields.

scholarly journals Compressive behaviours of octet-truss lattices

2020 ◽  
Vol 234 (16) ◽  
pp. 3257-3269 ◽  
Author(s):  
Yifan Li ◽  
Huaiyuan Gu ◽  
Martyn Pavier ◽  
Harry Coules
Keyword(s):  
Failure Modes ◽  
Density Ratio ◽  
Three Dimensional ◽  
Compressive Load ◽  
High Strength ◽  
Detailed Comparison ◽  
Compressive Response ◽  
Beam Elements ◽  
Structural Applications ◽  
Octet Truss

Octet-truss lattice structures can be used for lightweight structural applications due to their high strength-to-density ratio. In this research, octet-truss lattice specimens were fabricated by stereolithography additive manufacturing with a photopolymer resin. The mechanical properties of this structure have been examined in three orthogonal orientations under the compressive load. Detailed comparison and description were carried out on deformation mechanisms and failure modes in different lattice orientations. Finite element models using both beam elements and three-dimensional solid elements were used to simulate the compressive response of this structure. Both the load reaction and collapse modes obtained in simulations were compared with test results. Our results indicate that three-dimensional continuum element models are required to accurately capture the behaviour of real trusses, taking into account the effects of finite-sized beams and joints.

Numerical solutions for strain-softening surrounding rock under three-dimensional principal stress condition

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sheng Yu-ming ◽  
Li Chao ◽  
Xia Ming-yao ◽  
Zou Jin-feng
Keyword(s):  
Finite Element ◽  
Principal Stress ◽  
Stress Condition ◽  
Strain Softening ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Strength Criterion ◽  
Surrounding Rock ◽  
Flow Rule ◽  
Finite Element Software

Abstract In this study, elastoplastic model for the surrounding rock of axisymmetric circular tunnel is investigated under three-dimensional (3D) principal stress states. Novel numerical solutions for strain-softening surrounding rock were first proposed based on the modified 3D Hoek–Brown criterion and the associated flow rule. Under a 3D axisymmetric coordinate system, the distributions for stresses and displacement can be effectively determined on the basis of the redeveloped stress increment approach. The modified 3D Hoek–Brown strength criterion is also embedded into finite element software to characterize the yielding state of surrounding rock based on the modified yield surface and stress renewal algorithm. The Euler implicit constitutive integral algorithm and the consistent tangent stiffness matrix are reconstructed in terms of the 3D Hoek–Brown strength criterion. Therefore, the numerical solutions and finite element method (FEM) models for the deep buried tunnel under 3D principal stress condition are presented, so that the stability analysis of surrounding rock can be conducted in a direct and convenient way. The reliability of the proposed solutions was verified by comparison of the principal stresses obtained by the developed numerical approach and FEM model. From a practical point of view, the proposed approach can also be applied for the determination of ground response curve of the tunnel, which shows a satisfying accuracy compared with the measuring data.

scholarly journals Impact of partial slip and lateral walls on peristaltic transport of a couple stress fluid in a rectangular duct

2021 ◽  
Vol 104 (2) ◽  
pp. 003685042110136
Author(s):  
Safia Akram ◽  
Najma Saleem ◽  
Mir Yasir Umair ◽  
Sufian Munawar
Keyword(s):  
Couple Stress ◽  
Three Dimensional ◽  
Pressure Rise ◽  
Partial Slip ◽  
Couple Stress Fluid ◽  
Rectangular Duct ◽  
Peristaltic Pumping ◽  
Current Article ◽  
The Impact ◽  
Lateral Walls

The impact of lateral walls and partial slip with different waveforms on peristaltic pumping of couple stress fluid in a rectangular duct with different waveforms has been discussed in the current article. By means of a wave frame of reference the flow is explored travelling away from a fixed frame with velocity c. Peristaltic waves generated on horizontal surface walls of rectangular duct are considered using lubrication technique. Mathematical modelling of couple fluid for three-dimensional flow are first discussed in detail. Lubrication approaches are used to simplify the proposed problem. Exact solutions of pressure gradient, pressure rise, velocity and stream function have been calculated. Numerical and graphical descriptions are displayed to look at the behaviour of diverse emerging parameters.

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