The study is devoted to investigate the fatigue behavior and cracks development for both axisymmetric bars of circular cross-section smooth and notched specimens made of mild steel experimentally and analytically. The notch effect in fatigue is characterized by the fact that the notched specimen Wöhler curve is below the smooth specimen curve. Demonstration of the effect of notch on specimen uses Servo-Hydraulic Fatigue Testing Machine to perform fatigue test and the cracks derived are observed with a scanning electron microscope (SEM). The in-depth study of the stress distribution within the specimen is performed using computerized FEA analysis where the notched area is focused.
Fatigue is a progressive and localized structural damage that occurs when a material is subjected to cyclic loading in the form of axial, torsional and bending force. Fatigue failure occurs when a material is subjected to repeated loading and unloading and when it reaches certain threshold, where microscopic cracks will begin nucleate at the surface. Eventually the damage cumulates until a crack propagates to critical size, and the structure will suddenly fracture. Fatigue failure of a component typically occurs at a notch on a surface where the stress level increases due to the stress concentration effect. The term notch is defined as a geometric discontinuity that may be introduced either by design, such as a hole, or by the manufacturing process in the form of material and fabrication defects such as inclusions, weld defects, casting defects, or machining marks.
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Generally, there are three types of loadings that may present within a structure, namely, axial, torsional and bending. Each of these loadings affects the structure differently. Many studies have been carried out on the fracture and fatigue of notched effect on flat plate under torsional loading, but investigation on its effect on structure by axial is scarce. Axial loading is the most common type of load that involves a simple force that acts perpendicularly to the cross section of the structure.
With the help of state-of-the-art technology of Instron-8801, more reliable data can be obtained. The results generated shall be used to further confirm the viability of previous assumptions. Furthermore, more defined data may provide clues to the further understanding of the material and its reaction on fatigue loading.
2. Literature Review
Fatigue fracture generally occurs in 4 stages, namely, the crack nucleation, short crack growth. Long crack growth and final fracture. Cracks nucleation usually occurs on the localized shear plane at or near high stress concentrations, such as persistent slip bands, inclusions, porosity, or notches. The crack tends to grow along the plane of maximum shear stress and through the grain boundary. The next step in the fatigue process is the crack growth stage. This stage is divided between the growth of Stage I and Stage II cracks. Stage I crack nucleation and growth are usually considered to be the initial short crack propagation across a finite length of the order of a couple of grains on the local maximum shear stress plane. In this stage, the crack tip plasticity is greatly affected by the slip characteristics, grain size, orientation, and stress level, because the crack size is comparable to the material microstructure.
Stage II crack growth refers to long crack propagation normal to the principal tensile stress plane globally and in the maximum shear stress direction locally. In this stage, the characteristics of the long crack are less affected by the properties of the microstructure than the Stage I crack. This is because the crack tip plastic zone for Stage II crack is much larger than the material microstructure.
Theoretically speaking, based on the same high-cycle fatigue life, the fatigue strength of a smooth component should be higher than that of a notched component by the stress concentration factor, Kt which is highly dependent on the geometry of the notch. However, tests indicate that at the fatigue limit, the present of a notch on a component under cyclic nominal stress reduces the fatigue strength of the smooth component by a factor Kf. Tryon and Dey(2003) presented a study revealing the effect of fatigue strength reduction of Ti-6Al-4V in the high-cycle fatigue region. The Kf factor is called the fatigue strength reduction factor or the fatigue notch factor, and is usually defined as the ratio of the nominal fatigue notch factor, and is usually defined as the ratio of the nominal fatigue limits for smooth and notched test samples or components, i.e.,
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In general, Kf is equal to or less than Kt. The difference between Kt and Kf increases with a decrease in both the notch root radius and ultimate tensile strength. Both parameters can be empirically related by the notch sensitivity factor, q:
When q = 1, Kf = Kt and the material is considered to be fully notch sensitivity. On the other hand, if q = 0, Kf =1.0 and the material is considered to be notch insensitivity. This effect ia also called notch blunting effect where the discontinuity that present on the surface is negligible. This phenomenon usually occurs for condition where the surface damages exist are scratches or minor scars are negligible because of its depth compared to the size of the component is relatively small.
A plot by Peterson (1959) is provided in Figure 1 to determine the notch sensitivity for high-strength and low-strength steels. From the figure, it shows that the lower the ultimate strength of a material, the more exposed the material is to present of surface damages or discontinuity.
Figure 1 - Peterson's notch sensitivity curve for steel
Influence of the notch on the fatigue strength can be observed from figure 2. As the Kf factor increases, the endurance limit reduces exponentially.
Figure 2 - Fatigue Strength Reduction by Notch
Predicting the fatigue strength of a component requires the consideration of various factors besides notch effect. These factors include type of loading (CL), surface finishing (CS), size (CD), reliability level (CR) and fatigue limit (Se'). These factors are empirically range and are ranged between 0.0 to 1.0.
Analysis on the notch effect on mild steel circular rods is separated into 3 sections, namely, mechanical properties analysis, fatigue analysis and finally FEA stress simulation.
3.1 Mechanical Properties Analysis
Analysis on the mechanical properties of the specimen involves performing static loading on a sample material until a point where the specimen fractures. This experiment is performed on one specimen to obtain the stress-strain curve of the material. The dimension of the specimen is as illustrated below in figure 3.
Figure 3 - Specimen for Static Loading Analysis
This experiment involves utilizing the Universal Testing Machine (UTM). The machine is switched on and allows it to warm-up (approximately 15 minutes). Calibration is performed by the laboratory assistance prior to conducting the experiment. 2 lines measuring 50mm apart from the center of the specimen is drawn. These lines called the gauge length shall be the indicator of the final elongation of the specimen after it fractures. The bar specimen is then placed on the grip of the UTM and tighten it with the sequence of top first, and bottom last. Final confirmation is performed to make sure that everything is in the right position and the "START" button is executed.
Data were collected after the specimen fractures and is loaded into Microsoft Excel to plot the Stress-Strain curve. The mechanical properties of the material such as ultimate tensile strength, yield stress and etc. can be obtained via the curve. A sample of the curve is as shown in figure 4 below.
Figure 4 - General Stress-Strain diagram (Example)
3.2 FEA Stress Simulation
Failure due to static or dynamic loading usually occurs in the area of high stress concentration. Study on this region during loading may be performed via the computational FEA simulation. To perform this analysis, the geometry of the specimen is first developed with the help of CAD software (in this case, Solidworks is used). The designed specimen is then saved in a format IGS or STEP to be imported the design into the FEA analysis software. Meshing is done in the FEA software where the specimen model is split into thousands of basic geometrical shape to enable the calculation be done by the software. From here, various parameters are determined to enable the software to generate feasible data. After configured all required variables, the simulation model is inserted into the solver to perform calculation and generated visual results.
The results produced by the software solver are represented by color codes where red refers to high stress concentration and blue is the other way round. The region with concentrated red color is the location where the crack tends to initiate and will eventually propagates until the specimen fracture.
3.3 Fatigue Analysis
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Apart from the dynamic loading, conducting fatigue analysis is very much similar to that of the mechanical properties analysis. The specimens on the experiment involve 8 of each smooth, 1.5mm-notched and 2.5mm-notched circular rod. The detailed parameters are shown in figure below.
Figure 5: Smooth Specimen
Figure 6: Front View (1.5mm Notched Bar)
Figure 7: Side View (1.5mm Notched Bar)
Figure 8: Front View (2.5mm Notched Bar)
Figure 9: Side View (2.5mm Notched Bar)
To perform this experiment, Instron-8801 machine is used. Starting up the machine must be followed by machine warm-up where the machine is program to run dynamic loading without specimen for few minutes prior to conducting the experiment. Calibration of the machine is performed by the laboratory assistance before continuing with the experiment. The specimen is loaded onto the machine and the wave pattern of the dynamic loading is determined using the machine's control interface. After making sure everything is set, start the experiment. Observe the machine while the experiment is running and immediate stop the machine when the specimen fails.
After finished all 8 specimen for each parameter, the data extracted from each experiment is plotted using Matlab software. The curve plotted is called S-N curve and should look very similar to the figure 10. The curve decreases exponentially until a point where the curve becomes horizontal. This horizontal line is called endurance limit.
Figure 10: General Form of S-N Curve (Example)
4. Project Progress
Based on the gantt chart proposed, the progress as on the end of October should have achieved experimental stage. During this phase, experiment should have started to conduct upon specimens of mild steel prepared.
Up to this date, theoretical calculation has been performed to predict the possible outcome of experiment. Through the values obtained theoretically are utilized as the guidance for designing the experiment of fatigue analysis later on in mid of November. It also gives the insight of the result prior to conducting the test and what to expect after the experiment so that any possible error that may derived during the research may be corrected or avoided.
As for the preparation of samples, the design is based on specimens used in the experiment done by Hironobu Nisitani, Mesahino Goto and Hono Kawagoisi in year 1983. Due to the cost and duration of fabrication of the specimens, minor modification is done with minimal effect on the performance of the samples. A total of 39 specimens are fabricated with 10 pieces of specimens each for 1.5mm and 2.5mm notch bar and 19 pieces of smooth rod. There are 11 rejects or damaged specimens produced mainly due to inaccuracy of dimension and severe surface damage.