Dinamik çarpma problemlerinde malzeme seçiminin önemi

Abstract

Sunulan bu çalışmada, Bakır ve Çelik gibi iki ayrı malzemeden yapılmış silindirik bir modelin sürtünmesiz ve düzgün, rijit bir duvara önceden belirlenmiş başlangıç hızı ile dikey olarak çarpması sonucunda meydana gelebilecek şekil bozukluklarının incelenmesi amaçlanmıştır. Modelleme için Kaliforniya Üniversitesi Lawrence Livermore National Laboratory 'de geliştirilen DYNA3D isimli paket bilgisayar programı kullanılmıştır. Bilgisayar programı üç boyutlu olarak, dinamik yüklerin etkisi altındaki her türlü yapının davranışlarını, yapının içindeki gerilme dağılımını, yapıda meydana gelebilecek her türlü şekil bozukluklarını otuzbeş ayrı malzeme tipi tanımlayarak hesaplayabilmektedir. Bu araştırma için model olarak 3.24 cm uzunluğunda ve 0.32 cm çapındaki silindir örnek seçilmiştir. Sonlu elemanlar metodu için 4477 düğüm noktası ve 3888 prizmatik eleman kullanılmıştır. Örnek olarak seçilen modelin malzemesi elasto-plastik olduğunda modelde kalıcı şekil bozuklukları meydana gelmiş, şekil bozukluklarının düzeyinin modelin ilk hızına bağlı olduğu; eğer modelin malzemesi elastik olarak tanımlanırsa, o takdirde modelde herhangi kalıcı şekil bozukluğunun meydana gelmediği, çarpma şiddetine bağlı olarak geçici şekil bozuklukları olsa bile, çok kısa sürede modelin ilk durumuna döndüğü saptanmıştır.

Durability analysis in many Engineering fields such as Civil, Mechanical, Marine and Naval etc is mostly based on only static, laws. At present, Engineers know the importance of the dynamic investigation and qualification analysis, thus they cannot keep themselves away from this approach. It is difficult to determine the behaviour of an ordinary structure under dynamic loads varying with time, since the dynamic analysis is more complex than static one, and also requiring stochastic approach. Boundary conditions for any dynamic event show various characters due to a lots of parameters acting on the system. Some designers believe to ensure sufficient endurance with applying a number of correlation factors. The fact that must be remembered: The selected factors affect the economy and weight. The bigger the value of any selected factor is, the higher the total cost and also the heavier the weight of the construction are. The approach for the design of any construction having sufficient strength under different dynamic loads acting on it in the form of manual theoretical calculations, prototype manufacturing and testing can be extremely expensive in terms of time and money. The cost of developing this kind of system makes it essential for the Engineers to be able to forecast the behaviour of a proposed design through the utilisation of digital computers. Thus, CAD-Computer Aided Design and manufacture investigation programs and simulation models can be of great assistance to the designer and also the investor. The work presented in this thesis is concerned with the impact of the cylindrical projectile made of different vi materials, thrown perpendicular to a rigid boundary with different initial velocities. It is aimed to achieve the determination of the dynamic response of the model after impacting to the rigid wall and shape deformations occurred on its surface. Dynamic analysis with this subject dates back to the last half of 20 th Century when Taylor [1] studied the propagation of longitudinal waves inside of a short steel rod after impacting on a rigid boundary and he has developed an approximate formula which is related to the profile of the rigid plastic rod after impact with the dynamic yield point of material. Later, Wilkins and Guinan [2] together carried out a number of experiments in order to explain the relationship between the yield points of different materials and initial velocities. The computer simulation program named DYNA3D which was developed by the Methods Development Group of the Lawrence Livermore National Laboratory at California University, can be applied to transient dynamic problems from crash dynamics to human artery simulations. Thus, it has seen wide application to variety of problems over the past sixteen years. It is a nonlinear, explicit, finite element code for analysing the transient dynamic response of three-dimensional solids and structures. The code is fully vectorized and is available on several computer platforms. It includes solid, shell, beam and truss elements to allow maximum flexibility in modelling physical problems. The element formulations available to include one-dimensional truss and beam elements, two-dimensional quadrilateral and triangular shell elements, and three- dimensional continuum elements. Thirty five different material models are available to represent a wide range of material behaviour, including elasticity, plasticity, composites, thermal effects, and rate dependence. In addition, it has a sophisticated contact interface capability, including frictional sliding and single surface contact. Rigid materials provide added modelling flexibility. Versions of DYNA3D are available for several computing platforms, including CRAY/NLTSS, CRAY/UNICOS, VAX/VMS, and SUN/UNIX. The code has been ported to many other machines, and the use of X-Windows Graphics allows the SUN Version to port easily to other 32 -bit UNIX-based machines such as a CONVEX, SILICON GRAPHICS, or IBM RISC Workstation. The use of a "single-source" development system assures that all new developments appear simultaneously in all supported code versions. The computer simulation program DYNA3D includes the implementation of the YASE shell, the development of the interactive-graphics based material model driver for both solid and shell element material models, the incorporation of generalized Rayleigh damping for all element types. As an explicit code, it is appropriate for problems where high rate dynamics or stress wave propagation effects are Vii important. It may be applied to quasi-static problems by either using the dynamic relaxation option or by simply applying the external loads slowly and integrating the dynamics equations until all significant transients have died out. In this thesis, the computer simulation program DYNA3D is used to simulate a cylindrical bar impacting a rigid wall. The model consists of a long cylindrical bar with an initial velocity in the axial direction which impacts a rigid wall. Key features of this model is the use of an elasto-plastic nonlinear material model. The model which is shown in figures 3.1 and 3.2, consists of 4477 nodal points and 3888 solid brick elements. Hence, it is aimed to investigate the displacements and velocities of nodes on a cylindrical model at every time increments. Pre-selected model for this work has a cylindrical shape which is 0.32 cm in diameter and 3.24 cm in length. It is thrown perpendicular to a rigid wall fixed in space away from a distance of 0. 1 cm, with an initial velocity of 0.0227 cm/|j.s in the negative z-direction. Friction on the surface of the rigid wall is neglected and assumed that it has a smooth surface and there will not be any collapse on it after impact. At the beginning of this research, a bilinear elasto- plastic material model was used with the properties of copper. Isotropic strain hardening is included. Figure 3.3 shows the time history kinematic response of the nodal point 1 and nodal point 37. Node 37 is centrally located on the top x-y surface of the mesh, and node 1 is centrally located on the bottom of x-y surface of the mesh. The velocity response shows that the bar is fully decelerated just after 85 jisec. When the cylindrical model strikes perpendicular to the rigid boundary, a high stress occurs at the impact end. When the stress exceeds the elastic limit of copper, the plastic front moves back into the cylinder. The remaining elastic portion of the model flows to the plastic front, and shortens as copper flows radially out. The elastic portion of the model can support stresses no greater than the elastic limit. These stresses, which move between the plastic front and the free end, decelerate the model. The oscillations in the early portion of the response can be attributed to longitudinal shock waves which rapidly damp out. The displacement response shows a total z-displacement of -1.21 cm in figure 3.4. Thus, the final length of the 3.24 cm long bar is 2.13 cm. Hence the deceleration depends on the copper's strength; the greater the strength is, the faster the deceleration for an impact velocity of 0.0227 cm/^is. The variation of displacements of two nodes placed on the top and the bottom surfaces of the cylindrical bar, can be seen from the diagrams given in vxn Chapter 4. The material properties of copper are summarized as follows. Material Model Isotropic Elasto-Plastic Density 8.93 g/cm3 Elastic Modulus 1.17 g/|ls2cm Tangent Modulus l.OxlO"3 g/^s2cm Yield Strength 4.0xl0~3 g/|ls2cm Poisson's Ratio 0.33 Hardening Parameter 1 Later, a similar investigation is repeated for a steel rod which has dimensions same as the copper one. Unlike copper, steel is an elastic material. Under the same boundary conditions, this new model shows very different characteristics. There is no plastic deformation on the impact surface of the cylinder after striking and it regularly goes away from the wall but the velocities on both surfaces of the model shows a fluctuating characteristic. The displacement response of the nodal point 37 shows a total z-displacement of 0.24 cm in negative z-direction, in figure 3.6. Thus the final length of the 3.24 cm long bar is 3.14 cm. The variation of displacement of nodes 37 and 1 which are placed on the bottom and the top of the cylindrical bar, can be seen from figure 3.5. The velocity response shows that the cylindrical bar is fully decelerated just after 10 |isec and it resumes its original shape after 17 |j.sec. The stresses which move between the impact and the free ends make the steel rod to vibrate like a diapason. The material properties of steel are described as follows: Material Model Elastic Density 7.82 g/cm3 Elastic Modulus 2.06 g/|is2cm Poisson's Ratio 0.3 At the third step of this work, the steel rod is thrown perpendicular to the rigid wall fixed in space away from a distance of 0.1 cm, with an initial velocity of 0.05 cm/(is in the negative z-direction and the results of this process are shown in figures 3.7 and 3.8 At the fourth step, the initial velocity of the steel rod is selected as 0.1 cm/|is whilst the other boundary conditions and data are the same. The results of the fourth step presented in figures 3.9 and 3.10. IX The steel rod shows the similar characteristics even if the initial velocities are not same, since it is assumed as an elastic material. Finally, isotropic elasto-plastic model which is made of Copper impacts against the rigid wall with an initial velocity of 0.0227 cm/|is. The variation of normal and shear stresses with in the prismatic elements numbered 1 and 36 which are placed on the top and the bottom of the cylindrical rod are found with respect to time and their fluctuations are shown in Figures 3.11-3.16 If all diagrams and results are considered together, one can say that the deceleration of a cylindrical model is independent of the diameter of the cylinder for impacts against a rigid boundary whereas the flow stress of materials depends on work hardening, strain rate and temperature (dynamic effects).