Study the Effect of Cooling Rate on Fatigue Strength and Fatigue Life of Heated Carbon Steel Bars

The fatigue failure is the reason of (90%) of mechanical failures. This work tries improving the fatigue strength and increasing the fatigue life for steel bars that used in concrete reinforcing. Tensile test were done to find the mechanical properties of steel bar. The heating over critical temperature (AC3) and cooling by different cooling rates were done for steel bars, and tested this samples by tensile and fatigue tests. The tensile test results show increasing in yield and tensile strength for sample that cooled by oil (medium cooling rate).The fatigue test results show increasing in the fatigue life for samples that cooled by oil.


Introduction
Fatigue is referred to the degradation of mechanical properties leading to failure of a material or component under cyclic loading as shown in Figure 1.According to ASTM the standard definition of fatigue is the process of progressive localized permanent structural change occurring in material subjected to conditions that produce fluctuating stresses and strains at some point or points and that may culminate in crack or complete fracture after sufficient number of fluctuations (Andresen et al., 1997).
Figure 1.Shape of fatigue failure of steel shaft (Andresen et al., 1997) Fatigue strength of materials is often defined as the maximum stress amplitude without failure after given number of cycles.
It is estimated that about (90%) of service failure of metallic components resulted from fatigue.However, it is very time and money consuming to perform fatigue tests.Therefore, many attempts have been made to determine the fatigue strength in cost-effective way relating fatigue strength to other mechanical properties, such as yield strength, tensile strength, hardness (Pang et al., 2013;Murakami et al., 2002).
Engineers and scientists have proposed many formulas to describe the relations between fatigue strength and other mechanical properties (Murakami et al., 2002;Bathias et al., 2005;Lee et al., 2005).
In 1870s, Wöhler, one of the German pioneers in the fatigue field, found that the ratio of fatigue strength (σ f ) to tensile strength (σ t ) for ferrous metals followed a simple proportional relation as below: ' (0.4 0.5) ' Based on the numerous data of fatigue strength and tensile strength available for steel, aluminum, and copper alloys (Lee et al., 2005).
Fleck, study and determine the fatigue crack growth rate and crack closure response of steel under service loading at gas storage vessel.Crack propagation rates are found to be independent of specimen thickness.Crack growth is successfully predicted by linear summation using Paris law (Fleck et al., 1984).
Greger, study the deformation on low cycles fatigue of steel (AISI 316) by using (ECAP) technology and find the mechanical properties of steel samples by this technique, the fine grain sample of steel show shorter fatigue service life than the initial state samples (Kander, 2008).
Tilly, study the fatigue life and fatigue strength of reinforcing steel bar by using axial and bending fatigue tests and find that the endurance of steel bar influenced by type of steel, geometry , size of bars, and nature of cyclic loading and set the fatigue life of reinforced steel bar as shown in Figure 2 (Tilly,1979).

Experimental Materials and Work
The steel bar samples that used in this work had the chemical composition shown in Table 1.

Tensile Test
The tensile test were done according to specification (DIN 50125) to set the properties of steel sample like (young modulus, yield strength, and ultimate strength) by used the tensile test machine that shown in figure (3) and the sample dimension for tensile test shown in Figure 4.

Heating Process and Cooling
The heating process for samples done by used the electrical furnace; the samples were heated to temperature of (930 o C) to ensure the phase transformation then the samples cooled by using different types of cooling media as: (Arai, 1997;Yuce, 2007;Herring, 2007) 1) Very slow cooling (inside furnace):-The very slow cooling will provide the time to austenite microstructure to transform to pearlite structure that had good strength but low hardness.
2) Slow cooling (still air):-The advantages of using air are that distortion is negligible and that the steel can easily straightened during cooling process.
3) Medium cooling (by oil):-The medium cooling reduced likelihood of cracking.Problems associated with quenchants include water contamination, smoke and fire hazards.
4) Fast cooling (by water):-water is good quenching medium.It is cheap, readily available, easily stored nontoxic nonflammable smokeless and easy to filer and pump but with water quench the formation of bubbles may cause soft spots in the metal.Still other problems with water quench include its oxidizing nature, its corrosivity and the tendency to excessive distortion and cracking 5) High speed cooling by brine (salt+water):-Brine is a more severe quench medium than water.
Unfortunately, it tends to accelerate corrosion problems unless completely removed.
Cooling media and cooling rates had shown in Table 2.

Fatigue Test
The fatigue test for steel samples done according to specification (ASTM E467) by applied the bending load at the end of cantilever rotating sample with speed of (2000 rpm) of fatigue testing machine that shown in figure (5), and the sample of test prepared to final dimensions as shown in Figure 6.The bending load applied at the end of sample as (95N, 115N, 125N, 160N, and 200N).

Calculations
In most laboratory fatigue testing, the specimen is loaded so that stress it is cycled either between a maximum and minimum tensile stress or between a maximum tensile stress and specific level of compressive stress.The letter of the two, considered a negative tensile stress, are given an algebraic minus sign and called the minimum stress.The mean stress (σ m ) is algebraic average of maximum stress and minimum stress in one cycle: (Boardman, 1990) The range of stress (σ r ) is algebraic difference between maximum stress and minimum stress in one cycle: The stress amplitude (σ a ) is one-half the range of stress in one cycle: The stress ratio is the algebraic ratio of two specific stress values in stress cycle: The nominal stress in fully reversed bending loading test is: The fatigue fracture of structural details subjected to cyclic loads mostly occurs at a critical cross section with stress concentration.The stress concentration factor (K t ) for stepped shaft depend on the dimension of stepped sample as shown in Figure 7 (Pilkey, 1997).The fatigue stress concentration factor (K f ) depend on the value of stress concentration (K t ) and the notch sensitivity factor (q), that can found from notch sensitivity curve as shown in Figure 8.
So the value of actual fatigue stress equal to = Nominal bending stress *Fatigue stress concentration factor.

Tensile Test
Figure 9 shows the stress-strain diagram for steel bar at original state, from this curve the yield strength was (320 MPa) and ultimate strength (465MPa) and that refer to the steel bar is mild steel material that had good ductility properties.
Figure 10 shows the relation between the cooling rate after heating and the yield strength for steel bars, while Figure 11 shows the relation between the cooling rate after heating and the ultimate tensile strength of steel bars.These figures show that the better yield and ultimate tensile strength were for samples that cooled by oil at cooling speed (17 C o /sec), these refer to that the sample cooled with oil will have the microstructure of binite phase that had good tensile properties and good toughness.

Fatigue Test
Figures (12, 13, 14, 15, 16, and 17) show the (S-N) diagram for steel bar without heating and cooling , heating and cooling inside furnace (C.R = 0.11 Co/sec) , heating and cooling by air (C.R = 1.2 Co/sec), heating and cooling by oil (C.R = 17Co/sec), heating and cooling by water (C.R = 77 11 Co/sec), and heating and cooling in brine (C.R = 150 Co/sec).Form these figures can notice the behavior of steel under fully reversed cyclic loading (R = -1) , was better for samples that heated and cooling by oil (C.R = 17 Co/sec), while the endurance limit was constant were the better value of fatigue life was for samples cooled by oil that had longer fatigue life than other samples that cooled by other type of cooling media.The increase if fatigue life (number of cycles) happened as the cooling by oil gave binite microstructure for steel that had good toughness and harder to crack initiation on the sample surface that may growth to cause fatigue failure.The fatigue life for oil cooling samples increase (10 times) than the sample in original state, for water cooling samples fatigue life increased about (1.85 times), while it decrease for inside furnace ,still air, brine cooling samples as shown in Figure 18.

Conclusion
The Fatigue life of steel bar can improved by heating to (930Co) and cooling by oil about (10 times) of it for original state samples (without heating and cooling).
The medium cooling rate (by oil , water) gave best fatigue life than other type of cooling media.
The yield strength of steel bar increased about (17%) of the original state sample.
The ultimate tensile strength of steel bar increased about (16%) of the original state sample.
The lower values of fatigue life were for steel bar samples that cooled inside the furnace (very slow cooling rate).

Figure
Figure 5. Fatigue testing machine

Figure 9 .
Figure 9. Stress-strain diagram for steel bar

Figure 12
Figure 12.S-N diagram for steel bar without heating and cooling

Table 1 .
Chemical composition of steel bar