Temperleme sonrası çeliklerin sertliğini belirlemek için geliştirilen yeni bir yöntem - Sevük, Ahmet (Fen Bilimleri Enstitüsü, 1997)
eliklerin temperleme sonrası sahip olacağı sertliği verilen zaman ve sıcaklık koşullarında önceden hesaplayabilmek, pratikte önemi olan bir problemdir. Bugüne kadar yapılan çalışmalar, grafik esaslı olup, uygulaması zahmetli ve hassas olmayan ampirik çözümler olagelmişlerdir. Ayrıca, zamanın etkisi hesaplara tam olarak katılamamıştır. Daha da önemlisi, geliştirilen çözümler, genellikle martenzitik yapının temperlenmesiyle ilgilenmiş, farklı içyapıların davranışını tahmin edememiş ve çeliğin kimyasal bileşiminin etkisini basit bir biçimde hesaba katamamıştır. Bu çalışmada yedi farklı alaşımsız ve düşük alaşımlı çelikten hazırlanan Jominy numunelerine uçtan su verilerek, farklı soğuma hızlarıyla farklı içyapılar elde edilmiştir. Numuneler dört farklı sıcaklıkta temperlenerek, başlangıç sertliğinin nasıl değiştiği incelenmiştir. Temperlemenin, karbür parçacıklarının büyümesi ile sertlikte azalmaya neden olacağından hareketle, karbür büyümesi için yayınmanın sorumlu olduğu bir ifade kullanılarak, olayın matematik modeli çıkarılmıştır. Kimyasal bileşimin etkisi, kaynak tekniğinde kullanılan karbon eşdeğeri kavramıyla açıklanmaya çalışılmıştır. Sonuçta, zaman, sıcaklık ve kimyasal bileşimin etkisini tek bir formül ile belirlemek mümkün olmuştur. Ayrıca, geliştirilen formül ile başlangıç mikroyapısının etkisi normalize edilerek temperleme sonrası sertliği hesaplamak mümkün olmuştur. Yapılan deneyler ve kontroller sonrası, geliştirilen eşitlikte, zaman, sıcaklık, kimyasal bileşim ve başlangıç mikroyapısının etkileri biraraya getirilerek alaşımsız ve düşük alaşımlı çeliklerde ( ikincil sertleşme gösteren çelikler dışında), temperleme sonrası sertlik, 400-700°C aralığında (küçük bir değişiklikle 200°C'a kadar) hesaplanabilmektedir. Ayrıca, eşitliğin kaynak sırasında, Isı Tesiri Altında kalan Bölgede de aynı derecede hassas olduğu kanıtlanmıştır. Böylece tek bir eşitlikle, hızlı ve hassas bir biçimde temperleme sonrası sertlik elde edilebilmektedir.

Determination of hardness of steels after a tempering treatment has been a difficult problem in industry. For this reason, various investigations have been done to find a proper solution. Most of these studies were based primarily on graphics and the chemical composition of steels under consideration. The fundamental approach used in those earlier studies was to find the individual contributions of the alloying elements for the tempering temperature employed and to add them to reach the hardness after tempering. But these type of studies had also some common disadvantages. First of all, they were empirical studies and were valid for only a specific type of steel or for a specific range of alloying elements used in the research. Also, the tempering periods used in the studies were constant, so the determination of hardness for a longer or shorter period of time was very difficult. To overcome these difficulties, a solution involving Hollomon-Jaffe parameter was later incorporated. In spite of this, these " addition-based " methods were too tedious to work with. Another major disadvantage was that, with these methods one could find only the hardness of a " fully-martensitic " microstructure after tempering. Therefore, dependance of these empirical methods to some certain chemical composition ranges, tempering period and fixed prior microstructures, difficulty encountered with the graphical and tabular data and also, the inaccuracy of the earlier solutions rendered them insufficient. In the light of the above explained disadvantages, the aim of this study was to obtain a solution which can determine the hardness of a steel after tempering, no matter what the temperature, time and prior microstructure is. With the help of such a method, unnecessary waste of energy or time, therefore money, would be eliminated. Also, in welded components, since the hardness in the Heat Affected Zone ( HAZ ) should not be greater than a specific value to avoid the risk of cracking, it would be possible to predict the time and temperature of tempering treatment that should be employed to decrease the hardness below that certain level. In order to form the basis of the study, first, the fundamentals of the tempering treatment was examined. During tempering, various micromechanisms operate at the same time. But the result is nearly always the same. Apart from steels which can " secondary-harden " tempering causes " softening ". The reason behind this phenomenon is the growth and coalescence of carbide particles present in the structure. Consequently, the interparticle spacing increases and hardness XVI decreases. It has been found that hardness ( H ) is directly proportional to the reciprocal of the square-root of interparticle spacing ( X ): H a Xm ( 1 ) Therefore, during tempering hardness continuously decreases, while interparticle spacing increases. On the other hand, interparticle spacing is a function of the amount of carbide particles - that is the volume fraction of the carbide phase ( f ), and the diameter of the particle ( d ): ^ = k.f"1/2.d (2) However, for a given steel, during tempering volume fraction remains essentially constant and only the diameter of the carbide particle increases. Thus, if the growth rate of the particle diameter is known, the change of hardness during tempering will be determined. However, the carbide particles in steels have different shapes depending on the microstructure and their effects on hardening vary considerably. But, it was a common practice to assume a spherical particle shape and this helps in constituting a mathematical model more easily. Spherical carbide approach was also used in this study and particle diameter growth rule was taken as follows: d = a. ( D.t )m + do ( 3 ) Here, do, is the particle diameter before tempering, d, is the particle diameter after tempering, t, is time, D, is coefficient of volumetric diffusion, and a, is a function of supersaturation as in the case of quenching. This equation states that particle diameter increases via volumetric diffusion. After performing necessary calculations, the change of hardness after tempering was found as follows: (Ho/H)2-l=(a/do).t1/2.D1/2 (4) Here, Ho, is the initial hardness and H, is the hardness after tempering in Vickers Hardness Numbers. Moreover, coefficient of volumetric diffusion is a function of temperature ( T ): D = Do.e"Q/RT (5) Here, Q, is the activation energy of the process, R, is the universal gas constant and D0 is the frequency coefficient. Substitution of equation 5 into equation 4 yields: (Ho/H)2-l=A.t1/2.e-Q/2RT (6) Here A = (a/do). Do1/2 (hr."1/2), t is time (hr.), Q is the activation energy (J/mol), R is the universal gas constant (8.314 J/mol.K) and T is the absolute temperature (K). Equation 6 is the formula that gives the hardness of steels after tempering. With the help of equation 6, the effects of time and temperature of tempering are incorporated together in a single formula. XVll In order to find the unknown parameters - A and Q - and to evaluate the effect of chemical composition on these parameters, four plain carbon and three high strength low-alloy steels were selected. To determine the tempering behaviour of different microstructures, Jominy test was chosen, since the broad range of cooling rates encountered in Jominy tests yield a range of microstructures from fully martensitic to ferritic-pearlitic. Four specimens were machined from every type of steel and after Jominy tests were performed, hardness gradients were obtained by Vickers hardness measurements. Then, one of these four specimens from seven different steels were tempered for one hour at 400°C, one of them at 500°C, the other at 600°C, and the last one at 700 °C and the resultant hardness gradients were obtained. Then, five initial hardness values ( Ho ) were chosen arbitrarily for every type of steel and how these values changed after tempering ( H ) were determined graphically. Establishing the hardness ratios according to the reciprocal of absolute temperature yielded a change as follows: (H0/H)2-l=A.t1/2.e-B/T (7) When equation 7 was compared with equation 6, it was seen that, A = (a/do).D01/2 (hr/1/2) (8) and B = Q/2R (K) (9) From the last two equations, A and Q parameters were easily obtained. It was seen that activation energy was a function of the initial hardness ( Figure 1 ): Q = U.HoV (10) where U (J/mol) and V are constants, specific for the steel under consideration. But, V values were very close to - 0.5 and the relationships were re-established taking V values as - 0.5. On the other hand, A values were independent of Hq and essentially constant for the steel type being tested. Another remarkable consequence of the investigation was that, both Q and A values changed appreciably with the steel type, that is with the chemical composition. In order to incorporate the effects of alloying elements on the activation energy and A parameter, carbon equivalent concept which was previously used in welding technology was utilized.
A New method for the determination of hardness after tempering for steels
Tez (Doktora) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1997
Thesis (Ph.D.) -- İstanbul Technical University, Institute of Science and Technology, 1997
Keywords: Sertlik; Tavlama; Çelik-metal; Hardness; Annealing; Steel-metal