Çift eksenli gerilme altında parçalı hopkinson basma çubuğu ile malzeme analizi
Material analysis with the hopkinson pressure bar inbiaxial stress state
Yazar: SELİN GÜMÜŞ
Danışman: DOÇ. DR. EMİN SÜNBÜLOĞLU
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Makine Mühendisliği Ana Bilim Dalı / Katı Cisimlerin Mekaniği Bilim Dalı
Derece: Yüksek Lisans, 2019
Konu: Makine Mühendisliği = Mechanical Engineering

Özet:
Bu çalışmada Abaqus programı kullanılarak Parçalı Hopkinson deney düzeneği modellenmiş ve şişirme testi gibi bir düzenek tasarlanarak numunenin çift eksenli gerilme durumu altında malzeme özellikleri incelenmiştir.
Tasarım yapmadan önce malzeme özellikleri, yapılacak tasarıma uygun şekil değiştirme hızlarındaki karakteristikler hakkında bilgi sahibi olmak oldukça önemlidir. Malzemenin deformasyonu esnasında ortaya çıkan gerilme durumunun ya da malzemede oluşan deformasyonun, Sonlu Elemanlar ve benzeri yöntemler ile önceden tahmin edilmemesi veya hatalı şekilde öngörülmesi, hem maliyet hem de zaman kaybının artmasına neden olmaktadır. Bu amaçla zaman ve malzeme tasaruffu yapabilmek için de birçok yöntem geliştirilmiştir. Özellikle hidrolik şişirme (bulge), darbe testi ve iki eksenli çekme testi malzeme özelliklerini belirlemede kullanılan en yaygın yöntemlerdendir. Fakat bu yöntemler statik yüklemeye maruz kalan malzemeler için uygun olup yüksek şekil değiştirme hızlarına çıkılamamaktadır. Bu çalışmada yüksek şekil değiştirme hızları uygulanacağı için iki eksenli gerilme analizi yapılacak olup Parçalı Hopkinson Basma Çubuğu kullanılacaktır.
İlk olarak NX/Unigraphics programında modellenen düzenek Abaqus programına dahil edilerek giriş çubuğuna 15 m/s, 20 m/s ve 24 m/s büyüklüğünde üç farklı hız uygulanmıştır. Giriş çubuğunun oluşturduğu yansıma ve iletilen şekil değiştirme dalgaları yardımıyla Hopkinson formülleri kullanılarak numuneye ait gerilme-şekil değişimi ve deformasyon hızı- zaman eğrileri elde edilmiştir. Aynı şekilde numune için de gerilme-şekil değişimi ve deformasyon hızı-zaman grafikleri analiz sonuçlarından elde edilmiştir.
Hopkinson formülleri ile elde edilen grafikler ve numune üzerinden elde edilen grafiklerin birbirinden oransal olarak farklı olması sebebiyle Hopkinson formülleri ile elde edilen değerlerin sabit katsayılarla çarpılarak grafiklerin yakınsaması sağlanmıştır.
Elde edilen grafikler incelendiğinde malzemenin akma dayanımının 155-170 N/mm2 olduğu görülmüştür. Uygulanan hızın artmasıyla birlikte malzemede meydana gelen şekil değişimi ve deformasyon hızının arttığı görülmüştür. En yüksek deformasyon hızı 24 m/s uygulanan analizde gerçekleşmiş ve 3000 s-1 civarında olduğu gözlemlenmiştir. En yüksek şekil değişimi ise yine 24 m/s'de 0,18 olarak ölçülmüştür. En düşük deformasyon hızı ise 2000 s-1 ile 15 m/s hız uygulanan analizde görülürken, yine en düşük şekil değişimi 0,14 ile aynı hızda görülmüştür.
Yapılan çalışma sonucunda tasarlanan düzenek ile standart Hopkinson formüllerinin kullanılamadığı ve numuneye ait malzeme özelliklerinin elde edilebilmesinin ancak sabit bir katsayı ile çarpılarak mümkün olduğu görülmüştür.

Abstract:
In this study using Abaqus program Split Hopkinson Pressure Bar setup was modeled and additional setup was designed and material properties of the sample were investigated under the biaxial stress state.
Before making the design, it is very important to have knowledge about the properties of the materials and the characteristics of the deformations according to the design. The deformation of the stress caused during the deformation of the material or the deformation of the material, which is not predicted or incorrectly predicted by Finite Elements and similar methods, causes both cost and time loss to increase. For accurate modeling, tensile test is a commonly used method to study material behavior during loading. Tensile test is used in many engineering materials, including metals, to determine the relationship between stress and deformation of the material. In the tensile test, which is one of the most commonly used methods, the material is tested at a constant temperature (isothermal) and at a defined deformation rate on a single axis. Tensile test gives accurate results in the elastic region and in the plastic deformation where homogeneous deformation is observed, unless appropriate measurement methods are used. In addition, uniaxial tensile test results are insufficient to determine the behavior of materials, especially in the case of plane stresses. For this purpose, many methods have been developed to make time and material design. Especially, hydraulic bulge test, impact test and biaxial tensile test are the most common methods used to determine the material properties.
However, these methods are suitable for materials to static loading and high deformation rates cannot be reached. In this study, biaxial stress analysis will be performed as the high deformation rates will be applied and the Split Hopkinson Pressure Bar test will be used. In 1872, John Hopkinson first tested the rupture of a steel wire. In 1914, John Hopkinson's son, British electrical engineer Bertram Hopkinson, thought that the test methods used were inadequate to study the dynamic behavior of the materials and designed a rod to measure the high pressure generated by the explosive. In 1948, after the explosion, Davies used a parallel plate and cylinder capacitor to electrically measure the radial and axial movements of the Hopkinson rod. The Hopkinson Pressure Device developed by Herbert Kolsky in London in 1949 became the Hopkinson Kolsky Bar as it is used today. The general logic of the device starts with the generation of the tensile wave of the externally applied impact on the sample between the two elastic rods and the incident rod. When the tensile wave reaches the sample interface with the rod, some of it is transmitted back to the input bar as a wave reflected on the material and some of it continues on the material towards the output bar. The deformation of the material is calculated by means of the strain waves reflected in the reflected and transmitted waves and strain-gauge in the input and output bars.

It has been used in many studies since it is an observable test method for the investigation of the behavior of the material. In some studies, the reaction of the material under static and dynamic loading was observed, in others the effect of the deformation rate on the thickness of the material was investigated, and others were studied characterization of the dynamic damage occurring under different deformation rates.
In this study, stress and strain graphs of the material will be obtained by using Hopkinson formulas and finite element analysis method at different velocity and under biaxial stress. The use of physical models to solve engineering problems is very difficult in complex situations. Numerical modeling is used in cases where loading conditions are complex and the effects of many variables need to be examined. In case of material problems with complex geometries, which have different material properties and under different loading conditions, realistic results are obtained by seperating the model into pieces.
Firstly, the apparatus, which was designed to investigate the effect of different strain rates on the sample and mounted on the Split Hopkinson Pressure Bar, was designed to be producible and adaptable to the test apparatus. The apparatus was formed with seven main part and these are the force bar, the outer cylinder, the screws, the supporting cylinder, the water volume, the sealing member and the sample. After design, parts are divided into elements (mesh) for finite element analysis. The element geometries can be one-dimensional, two-dimensional, rectangular, triangular or three-dimensional, hexahedral, pentahedral, or tetrahedral. In this study, two different element geometries are used and these are hexahedral and quadrilateral element types. However, before the element geometry was created, the geometries of the parts were simplified so that each element assigned to the parts had optimum geometry for numerical solution. The indentations that will not be examined in the analysis were destroyed, bolt geometry was simplified and sharp corners were avoided and contributed to the analysis solution. In the next stage, materials were assigned, contact conditions were determined and boundary conditions were established. In order to control the operation of these features, fluid volume and the whole apparatus assigned to the parts, the analysis was statically solved at the first study. After the system verification, the Hopkinson Pressure Bars were included in the analysis and the necessary features were assigned and the analysis was performed with explicit solution method under different speeds as 15 m/s, 20 m/s ve 24 m/s. The equations to be calculated for each element in the model to be analyzed can be solved with the help of implicit and explicit analysis methods. Implicit solution technique is used for static and low speed analysis; explicit solution method is used to simulate high velocity and nonlinear dynamic events such as automobile collision and ballistic effect. For this reason, in this study, the explicit solution method was used since high velocities were applied to the sample.
The stress-strain and strain rate-time curves of the sample were obtained by using Hopkinson formulas with reflection and transmitted strain rate waves created by the input bar. Similarly, the stress-strain and strain rate-time graphs of the sample were obtained from the analysis results.
The graphs obtained by the Hopkinson formulas and the graphs obtained from the sample were proportionally different from each other. Therefore, the values obtained by the Hopkinson formulas were multiplied by the constant coefficients and the graphs were converged.

When the obtained graphs were examined, the yield strength of the material was found to be 155-170 N/mm2. It has been seen that the strain rate changing in the material increase with increasing of velocity. The highest strain rate was obtained at 24 m/s and the value was observed nearly 3000 s-1. The highest deformation was measured as 0,18 at 24 m/s. The lowest strain rate was obtained at 2000 s-1 and was observed as 15 m/s. The lowest deformation was seen at the same speed as 0.14.
It was seen that the standard Hopkinson formulas could not be used and the material properties. The material properties of the sample can be obtained only by multiplying with a fixed coefficient.