Research On Efficient Numerical Simulation Technique For Mechanical Behavior Of Wire Strands

Wire strands typically comprise groups of wires spun helically in successive layers over a straight center wire in a regular geometric pattern and they constitute a class of important engineering components.In recent years,with the improvement of twisting technique and wire property,the number of strand wire layers has been increased and the capabilities of axial load bearing,anti-rotation,corrosion resistance and high temperature have also been improved.Thus the use of wire strands has a bright prospects of application.The connection performance of wires strands is determined not just by the mechanical properties of strand itself,but also by that of strand ends.Socket casting end is widely applied in the engineering application and wire rope/strand test.Its mechanical properties are the same as that of the strand itself which directly determines the safety and stability of the machinery equipment,operators and enigineering structures.Therefore,it is very significant to develop efficient and accurate numerical simulation technique to study the mechanical behavior of wire strands and their end structures.According to the rules and national standards of the tensile experiment for wire ropes and strands,a sample of the six layered 91-wire strand is preparated and a suitable test plan is devised.Using the hydromatic tension machine DL-5000,the tensile test on the six layered 91-wire strand is conducted.The experimental data which denote the tensile properties of the wire strand are measured by using the specialized test equipment and the data measurement system.The data analysis and data processing are implemented and it provides the verification basis for the subsequent simulation analysis.Based on the Hertz contact theory for contacts between two spatial cylinders,the relationship of the normal contact force and the approach of contacting wire centerlines for inter-wire contacts inherent in the strand structure is established.The contact force occured between contacting wires in arbitrary two adjacent layers is also derived via the analysis of the characteristics of the strand geometry and inter-wire contacts.Based on the works noted above and Costello's analytical model,a nonlinear analytical model for wire strands is presented.This model is capable of taking into account the nonlinear factor of contact deformation caused by inter-wire contact in detail,thus the calculation precision for the prediction of the strand axial tensile properties is improved.Quasi-Newton numerical method has been adopted to solve the analytical model and good computional efficiency is achieved.By using the model developed,the tensile behavior of a six-layered 91-wire strand has been analyzed.Compared with Costello's analytical model,the numerical results predicted by the newly developed analytcial model show good agreement with the experimental data obtained from the tentile test conducted on a six layered 91-wire strand.Using two-noded elastic-plastic beam elements for wire discretization and Hertz contact elements which are developed based on Hertz contact theory for the simulation of contacts between wires,a beam finite element model(FEM)for wire strands is developed.The major influencing factors such as wire diameter contraction due to Poisson's ratio,wire uneven beding effect caused by discontinue contact points,contact deformation caused by inter-wire contacts and wire material plasticity are all considered.Two numerical examples of a three layered 19-wire strand and a six layered 91-wire strand are presented to validate the newly developed beam FEM.The axial tensile properties of the examples noted above have been analyzed.The finite element analysis results show that the results obtained from the three layered 19-wire strand model are in good agreement with those obtained from the accurate full three-dimensional solid FEM.The degrees of freedom of this model is only about 4% of the solid FEM and the computional time is approximately 20%,which greatly reduces the model size and increases the computiaonal efficiency.The numerical results predicted by the six layered 91-wire strand model show better agreement with experimental data than Costello's analytical model.Based on the domain superposition technique(DST)for efficient modelling of complex composite structures and composite materials,a three-dimensional solid FEM for a strand with a socket casting end is developed.The actual geometry and material proeperties of dispersed wires and iron serving wires,which are inserted into the casting end,are considered in detail.Moreover,in oder to improve the calculation accuracy,nonlinear effects including material plasticity of each part of the socket casting end,contact between wires,contact between the socket internal cone surface and the composite casting end surface and friction between these contacting surfaces are all taken into account in this model.By using the DST method,the difficulties of dealing with the complex inner architecture of the casting end in the conventional modeling process are avoided skillfully.The detailed axial tension properties of a 7-wire strand with zinc alloy filled socket termination has been predicted efficiently by using the newly developed model.The numerical results show that the socket casting termination structure is capable of bearing an aixal load level as high as the breaking load of the wire strand itself.For the special socket termination structural considered,its design could be very conservative.The region affected by the termination effect of the socket casting ends is approximately two times of the 7-wire strand diameter.In this region,both the contact force and relative sliding between wires outside socket exist at the same time,which is most likely to result in fretting fatigue.