Fracture Analysis of a Hook - Assignment Example

FRACTURE ANALYSIS By Student’s name Course code and name Professor’s name University name City, State Date of submission Introduction Material strength can be established through the failure theory which is used to study the structural design in order to determine safety of equipment prior to production. Once a material cracks or forms a flaw there is a tendency for it to fail at a stress that is lower than the threshold material strength. It is therefore for engineers to institute studies meant to demystify the levels to which materials can withstand flaws given the factors of safety are important elements towards decision making. This can therefore be reached at by use of solid mechanics programs such as ANSYS to establish fracture toughness for various materials that are likely to be deployed for any given engineering designs. With this regards, this assignment studies the effects of a 12mm crack on a hook template with a 115mm outside diameter and 75mm inside diameter. In order to determine its fracture toughness, it is assumed that the crack happens within its semicircular segment’s center line. A load of 5KN is applied to the analysis model so as to establish the stress intensity factors as well as compare to the existing theoretical formulae. Finite Element Analysis While the aim of this assignment was to test on the software skills accrued over time in the use of ANSYS, the theoretical approach was also deployed. The aim of this finite element analysis was to establish the most applicable method in finding solutions for practical fracture problems that exist within the engineering environment. The approach utilized in coming up with a solution for this problem was basic ANYS Parametric Design Language (APDL). This program is based on singular element analysis; a behavior that can only be achieved via use of quadratic element thereby reaching at the three conjoined nodes to analyze a crack tip node. This is done on assumption that the material is homogenous is likely to behave in such a manner depicting the surrounding crack tip in the LEFM as a spider web to be used in carrying out an elasto-plastic analysis (Gunawan, 2015). Figure 1 a: Singular elements surrounding the crack tip. Figure 1b: Arc shaped specimen forming the semicircular segment of a lifting hook. This analysis model is based on permitted ASTM standards whose crack initiation and development according to T.L. Anderson (2005) allow for five configurations e.g. standard notched bends, disk specimen, middle tension among others. Figure 1b above shows the specimen form that was used in the solid modelling of a load handling hook for fatigue analysis. In ANSYS a singular element is generated by using the tip location prior to generation of a mesh is generated for analysis purposes. For a center cracked hook specimen in consideration, the stress intensity factor can be directly calculated using the stress intensity equation stated below which has also been integrated within the ANSYS program; Where P is the applied load also put into consideration while formulating assumptions to be used in the modelling analysis, while can be stated as; The following are some of the screenshots that are generated from this highly integrated analysis software right from scratch to the advanced stage. Figure 2: The concentric model of the analysis mesh was achieved quite easily by inputting the required data and executing the commands as required. Figure 3: Mesh of a small portion of the concentric cracked tension segment. Figure 4: Finite element mesh of the center cracked tension specimen after applying a load of 5KN. Figures 5, 6 & 7: The spider-mesh surrounding the crack tip. Figure 8: A screen shot of the deformed segments. Assumptions The major assumption of this study is that the disc shaped area’s compact segment shall be analyzed for establishment of stress constants that results off this modelling exercise in order to make it easy to generate a working model. While a majority of fracture toughness tests are performed using single-edge-notched SE(B) specimen and compact specimen, this modelling exercise is not an exception. A compact specimen is pin-loaded using special clevises in real life scenario and this also applies in the case of the ANSYS exercise where fixture dimensions definitions are based on the real life models (T. L. Anderson, 2005). Further to this, the compact specimen can be used to indicate geometric scales which cannot be deployed in other models. In this case the theoretical approach indicates all the dimensions deployed in this exercise and the anticipated results. Theoretical Approach Where; Calculating for g; Assuming that; Crack length (2a) = (5+2) mm Plate width (2W) = 40mm Calculating for K1 Where; Crack length (2a) = (5+2) mm Plate width (2W) = 40mm X = 75mm (assuming the load is acting towards on the hook’s center line) Plate thickness B = 10mm Discussion The equations provided above cannot be used to deduce the intensity factors as is applicable in APDL ANSYS. This is based on the argument that, while the equation is supposed to be homogenous in the sense that all bits of the equation are supposed to balance, in order to achieve K1 from either substitution or multiplication, this does not suffice. The equation below can comfortably be substituted instead; Applying the equation above which has also been implemented in an ANSYS-APDL code will return the stress intensity factors for given some necessary data as per summary given below. (Gunawan, 2015), (T. L. Anderson, 2005). Conclusion The assignment was carried out in a quite easy manner as all the required details were supplied within the assessment files specifically when it came to issuing commands. The results segment was however a bit confusing as I could not freely generate the required results data table thus making it difficult for the discussion section to yield the expected outcome. Feedback that can assist in coming up with better assessments should be aimed at use of more common software such as Solid Works to issue instructions. Other than this the knowledge achieved shall go a long way in improving personal skills of the order of 3D modelling and simple 2D modelling. References Gunawan, F. E., 2015. LEFM Analysis of a Center Cracked Specimen, Aichi: Toyohashi University of Technology. T. L. Anderson, 2005. Fracture Mechanics: Fundamentals and Applications, Third Edition. 3rd ed. London: CRC Press. Read More