178
TECHNICAL UNIVERSITY OF CLUJ-NAPOCA
ACTA TECHNICA NAPOCENSIS
Series: Applied Mathematics and Mechanics
53, 2010
Upon Accompanying of the Experimental Testing
of Materials by Numerical Analysis with FEM
Vasile NĂSTĂSESCU, Nicolae ILIESCU
Abstract: Different materials, from iron or non-iron to plastics materials, are used more and more even in those conditions where safety requirements must be full filled, in static and dynamic conditions. Using of the plastics materials is based on their properties, which were essentially improved in last period.
This paper presents the numerical simulation, by Finite Element Method, of two dynamical mechanical tests: Charpy and Izod. Special material models of materials were used for simulation of the material failure. Material models like Plastic-kinematic (Cowper-Symonds), Johnson-Cook, Modified Johnson-Cook, Picewise linear plasticity, Modified picewise linear plasticity and many others are available in many professional codes. Without such material models, a right numerical simulation, including the fracture description, is not possible.
After numerical modeling of the mechanical test in a very good concordance with the experimental results, many different numerical studies were made regarding to the influence of the constructive or modeling parameters.
These numerical simulations are very useful in the process of improving of the mechanical properties and they allow us to compare different types of materials etc.
One of the conclusions is that the numerical simulation of dynamic mechanical tests is a way of enriching our knowledge about material, no matters of material types.
Keywords: Izod test, Charpy test, notched specimen, finite element, material model
178
1. Introduction
Nowadays, knowledge about material behaviour under dynamic loading are more and more important, because such loads are met in a lot of industrial structures, in a lot of machineries, in a lot of many special structures. On the other hand, the number of material types increased; next to usual steel materials a lot of other materials, especially plastics materials are used more and more. For a safety drawing and for a properly working, the properties of such materials have to be known. The Charpy test gives us information about dynamic behavior of a material.
The Charpy impact test was invented by Georges Augustin Albert Charpy (1865-1945). This test measures the energy absorbed by a standard notched specimen while breaking under an impact load. This test appears to be, from a syecle ago up to nowadays, an economical quality control method to determine the notch sensitivity and impact toughness of engineering materials. The Charpy test is commonly used on metals, but is also applied to composites, ceramics and polymers. The standard Charpy Test specimen consist of a bar of metal, or other material, 55x10x10mm having a notch machined across one of the larger dimensions. This notch can have the “U” or “V” shape. All conditions are regulated by standards of different countries.
The Izod impact test was invented in the early 1900's by a metallurgist named Izod. The Izod test consists of a pendulum with a determined weight at the end of its arm swinging down and striking the specimen while it is held securely in a vertical position. This is the primary difference between the Izod and the Charpy test. The Izod test differs also in that the notch is positioned facing the striker.
The impact strength is determined by the loss of energy of the pendulum as determined by precisely measuring the loss of height in the pendulum's swing.
The standard Charpy Test specimen consist of a bar of metal, or other material, 55x10x10mm having a notch machined across one of the larger dimensions. Izod test is used specially in North America and Charpy test is used specially in Europe. As plastics materials are concerned, Izod test is most used.
The Charpy impact test continues to be used as an economical quality control method to determine the notch sensitivity and impact toughness of engineering materials. The Charpy Test is commonly used on metals, but is also applied to composites, ceramics and polymers.
Taking into account above considerations, this paper offers some models, methodologies and examples referring to the numerical simulation of these two dynamical tests, Charpy and Izod. Many other aspects are also presented. Therefore, the numerical simulations of the mechanical tests, especially dynamical tests, seem to be a proper way of improving of the test results.
2. Material Models Used for Numerical Simulation
One of the most used material model, adopted for the specimen or target (often for the projectile or hammer too), is the Elastic Plastic with Kinematic Hardening Model, being strain rate dependent plasticity for isotropic materials. The strain rate is taken into account by Cowper-Symonds model using the coefficients C and P, having the same name.
The yield function is given by [1]:
(1)
where is the initial yield stress, is the effective plastic strain, is the plastic hardening modulus, which is given by:
, (2)
being the hardening parameter that can vary between zero and one depending on plasticity type (zero for kinematic and one for isotropic respectively) and ET is the tangent modulus. For this model, the user has to specify the failure strain for which elements will be eliminated.
According to the flow rule, the direction of plastic straining can be evaluated. The hardening rule describes the changing of the yield surface with progressive yielding, so that the conditions for subsequent yielding can be established.
Another material model equally used for specimen (target) and hummer (projectile) modeling is Johnson and Cook Plasticity Model, [1], which express the flow stresses:
(3)
where A, B, C, n, and m are user defined input constants,is the effective plastic strain, and:
(4)
is the effective plastic strain rate for =1 s-1, and:
(5)
T being the temperature (by empirical assumption T represents 90% of the plastic work, Troom is the room environment temperature and Tmelt is the melting temperature of the material).
The strain at fracture is given by: (6)
where D1…D5 are input constants and is the ratio of pressure divided by effective stress:
(7)
Fracture occurs when the damage parameter
(8)
reaches the value 1.
An other material model, an elasto-plastic material with an arbitrary stress versus strain curve and arbitrary strain rate dependency can be used.
The failure is defined by a plastic strain or a minimum time step size. The stress strain behavior may be treated by a bilinear stress strain curve by defining the tangent modulus, or, by a curve of effective stress vs. effective plastic strain. Strain rate may be accounted by using the Cowper and Symonds coefficients ( and ) like in relation (1), which scales the yield stress with the factor ,
(9)
where is the strain rate. If the viscoplastic option is used and if then the dynamic yield stress is computed from the sum of the static stress, , which is typically given by a load curve and the initial yield stress, , multiplied by the Cowper-Symonds rate term as follows:
(10)
For hummer (striker) modeling Rigid Material Model [1] is often used. Such approximation of a deformable body is a preferred modeling technique in many real work applications, because the calculus time can be significant smaller. In many cases we are interested in what happens with the target and fewer with the projectile.
The elements which are considered rigid are bypassed in the element processing and no storage is allocated for storing history variables, so the rigid material model is a very cost efficient one.
Some material properties have to be given by the user. Young’s modulus E and Poisson’s ratio are used for determining sliding interface parameters if the rigid body interacts in a contact definition.
Density is necessary for calculus of the inertial properties. In all cases, it is useful to know that unrealistic values of the material constants may cause some solving difficulties.
3. Cowper-Symonds Coefficients
For using of the elastic-plastic with kinematic hardening material model, or any other material model which takes into account the strain ratio, a very difficult problem is the choosing of the material constants C and P (Cowper-Symonds –Jones coefficients).
The best way is the experimental one, but often it is not possible because of varying reasons. If the material characteristic curve (under dynamic conditions) is known (strain rate is also known), then it is possible constants C and P to be determined.
It is very useful to make some comparing between different materials; next to it, it is also useful to know which is the influence of each constant upon the yield stress - relation (1) - and how the up or down of C or P constant determines the level of the yield stress.
For a common steel, such dependences are presented in the figures 1 and 2. As we can see, a right choosing of the constant P is very important because the value of the yield stress is strongly affected.
Fig. 1 The influence of the constant C
Fig. 2 The influence of the constant P
In the considered example, for the C=50 and strain rate of 2000 s-1, for P=2 the initial value of the yield stress is multiplied by 7.32 times, and for P=7 the multiplying factor is 2.69 only.
In the same conditions, but for P=4, the ratio sy/so - relation (1), moves from 3.17 for C=90, to 4.76 for C=10.
Therefore, only a right value for each coefficient C and P could lead us to a right results.
A similar study can be made referring to other coefficients (Johnson-Cook Plasticity Model) which take into account the strain rate. Such study needs much more considerations, being over the target of this paper.
4. Finite Element Model
Finite element modeling was made taking into account the structure symmetry (Charpy test), the possibility of modeling of the material fracture, the contact characteristics and others parameters, which to describe the test in a closed concordance with the reality.
Fig. 3 Finite element model for Charpy test
The model is a 3D one and it is limited only to that zone of the impact. For instance, only a part of the hummer (striker) is modeled, but using a material density which to ensure the real energy of the striker. The specimen was completely modeled and restrictions applied were in a strictly concordance with the reality.
As the installation is concerned, only a little part of it was modeled, namely, only that part referring to the clamping or sitting of the specimen.
Fig. 4 Finite element model for Izod test
Fig. 3 and 4 present the finite element model for those two tests, Charpy and Izod. In the case of Izod test, for plastics materials, the specimen had both subsize dimension (2.5 mm thickness) and normal dimension (10 mm thickness) and a “V” notch. For Charpy test, the specimen had both standard notches, “U” and “V”.
For these two finite element models, finite element SOLID 164 of the Ls-Dyna finite element library was used and the mesh was a nonuniform one. In the vicinity of fracture zone, the element size is about 0.1 mm.
For Izod test simulation (Fig. 4), as we can see, the specimen is fixed (clamped) in a device and different levels of the clamping pressure were considered. So, the influence of stress field near the notch prior to impact was analyzed. This aspect represents a disadvantage of the Izod test.
The numerical simulation of Charpy and Izod tests, for plastics materials, was based on a tester having pendulum impact energy of 15 joules, weight of pendulum of 4.67 kg and a striking velocity of 2.45 m/s.
The numerical simulations were performed in accordance with ASTM D256 and ISO 180 for Izod test and in accordance with ISO 179-1 for Charpy test. For striker modeling rigid material model was used. The analysis time was 4 to 15 milliseconds.
5. Results
The numerical simulations were made for steel and plastics materials. Using a steel with the characteristics presented in the below figure, and a specimen with “U” notch, some dependences between material characteristics and test results were established.
Fig. 5 Deformed shape and von Mises stress field distribution for a Charpy test
Figure 6 presents the Charpy test results, for a material, for some values of the C and P coefficients. The dependence between yielding stress of the material and Charpy test result is presented in the figure 7.
Fig. 6 Charpy test results for different
C and P values
Fig. 7 Dependence between yielding stress and Charpy test result
The Izod test was used for a plastics material. The characteristics of the plastics material studied (Nylon 6 with 30% glass-fiber filled) are presented in the below table (Table nr. 1), the data being supplied by the manufacturer.
Table 1
The properties of Nylon 6 with 30% glass-fiber filled
No. / Properties / Values / Measure units1 / Density / 1.35 / g/cm3
2 / Tensile strength (ultimate stress) / 195.00 / MPa
3 / Elongation at break / 10.00 / %
4 / Yield stress / 140.00 / MPa
5 / Elongation at yield / 6.00 / %
6 / Tensile modulus / 11.10 / GPa
7 / Poisson’s ratio / 0.35 / -
8 / Izod impact, notched / 2.40 / J/cm
9 / Charpy impact, notched / 3.50 / J/cm2