The method for lifetime estimation through the mechanical properties in tension Текст научной статьи по специальности «Строительство и архитектура»

© Bakhracheva Yu.S., 2014

ТЕХНИКО-ТЕХНОЛОГИЧЕСКИЕ

ИННОВАЦИИ

УДК 669.0 ББК 34.2

THE METHOD FOR LIFETIME ESTIMATION THROUGH THE MECHANICAL PROPERTIES IN TENSION

Candidate of Technical Sciences, Associate Professor, Department of Physics and Chemistry, Moscow State University of Communication Means (MIIT), Volgograd Branch bakhracheva@yandex. ru

Bukhantseva St., 48, 400120 Volgograd, Russian Federation

Abstract. The method for prediction of Paris’ curve shape through the results of tensile test is suggested. For this purpose the author developed non-direct method for determination of AK h and SKfc and corresponding to them da/dN values. The relationship between AK h and ab/<5y ratio was found. The correlation AKfc(K/c) was also shown. It makes possible to estimate lifetime of different structures with cracks under cyclic loading.

Key words: Paris’ curve, cyclic loading, lifetime, non-direct method, tensile test.

Bakhracheva Yuliya Sagidullovna

Introduction

for an extended useful time. Applying the fracture mechanics principles makes possible to predict the number of cycles spent for crack growth to some specified length or to final failure.

For many years attempts have been made to understand the crack growth mechanism and predict lifetime under conditions of cyclic loading. Cracks exist in many structural components. The crack growth resistance is an important property of the material which controls the lifetime of the component. Studies on the growth of cracks have led to the observation that fatigue life of many engineering materials is primarily dependent on micro-structural features, such as inclusion particles, voids, slip-bands or manufacturing defects. Thus, knowledge of the crack rate makes possible the prediction of residual lifetime of a component. Due to that cracked component may be kept in service

This curve may be divided into three regions (fig. 1). At low stress intensities, Region I, cracking

behavior is associated with threshold, AK,

th

effects. By considering the term AK h the designer can ensure that no crack growth will occur. AK h is the “fatigue crack growth threshold”, and signifies the critical value of AK below which

Determining the critical cyclic loading conditions is commonly performed by using a Paris’ curve. The Paris’ curve is dependence of crack growth rate, da/dN on the stress intensity

crack growth will not occur. It is calculated using the Paris’ curve, and is the value of AK corresponding to da/dN = 0. In the Region III, at high AK values, crack growth rates are extremely high and little fatigue life is involved. Finally, in the mid-region, Region II, the curve is essentially linear and can be described by the Paris’ equation

da / dN = C( ЛK )n

(1)

where C and n are material constants and AK is the stress intensity: AK = K - K .

J max min

However, the procedure for Paris’ curve determination by means of direct testing is enough complicated and expensive. Sometimes, it is just impossible, for example in cases when structures or equipment are under exploitation conditions.

Therefore many investigators made large efforts to develop models for Paris’ curve shape predicting. The relationship between fracture toughness, AKfc and KIc, AKfc and KId was shown in paper [4; 6]. The correlation between constants C and n in the Paris’ equation is known [3; 7]. But up to date there is no model for AKth and constants n and C in Paris’ equation predicting.

Our approach to this problem is presented below.

Analysis

The simplified shape of a Paris’ curve is presented on fig. 1.

As can be seen from this figure, the reconstruction of a curve linear Region II may be done if the AKth, AKfc, and corresponding to them da/dN values are known. It makes possible to calculate constant n in Paris’ equation as:

n = (lg Vfc - lg Vth ) / (lg AKfc - lg AKth ) (2)

where vth and v^ - the crack propagation rates corresponding to AKth and AKfc.

Crack propagation rates in eqn. (2) are not known.

For this reason the assumption is accepted that the crack propagation rate is proportional to the small scale yielding zone width. In this case it makes possible to rewrite the eqn. (2) in the following form (3):

n = (lg rfc - lg rth) / (lg AKfC - lg AKth), (3)

where rh and rfc are the small scale yielding zones corresponding to AKth and AKfc. The rfc and r, values are determined as:

(1 - 2ц)2

2n

r,, =

(1- 2ц):

2 (

2л

(4)

(5)

where ц - Poisson’s ratio, Sk - fracture stress.

In the eqn. (5), the substitution of an Skvalue instead of oy is accounted for by the following reason. The ЛКл determination procedure is carried out under conditions of a load decreasing. Thus, the crack propagation in this region is accomplished in the extremely hardened material.

It can be seen from eqns (3-5) that for the purposes of further analysis it is necessary to develop the non-direct methods for ЛКЙ and ЛК^ determination.

Discussion

We have proved the existence of a linear correlation between fracture toughness, Кл, and ЛК^ values for more than 40 different steels [5]. This relationship is shown on fig. 2 and is described by the following equation:

Fig. 1. The simplification of Paris’ curve

ЛKfc = 0.8611 • Klc - 26.387.

(б)

2

2

MPa*m

0.5

Fig. 2. The relationship between Кc and ЛК

Previously [1; 2; 8] the practical methods for fracture toughness KIc prediction through mechanical properties in tension and hardness values of materials were developed. The predicted KIc value may be used for AKfc calculation through the eqn. (6).

The results of calculation AKfc are presented in table 1.

In this work also the relationship between AKth and ^b/cy was proposed (fig. 3).

It is valid for many different steels [4-6] and may be described by linear function:

AKth = 36.906 -ct4 / ct, - 34.04, (7)

where CTb is an ultimate tensile strength, CTy is a yield stress.

The results of AKth calculation are presented and compared to their experimental values in table 2.

It should be noted however that determining AKth values is dependent on testing equipment.

Now, when the AKth h AKfc are already found, the n constant value in the eqn. (3) can be calculated. After that we have to find the C constant in eqn. (1).

The correlation between constants C and n in the Paris’ equation is known [3; 7]. We have confirmed this relationship for steels investigated in present paper. It can be described as:

C = 0.0002 •

(S)

The fair of this formula was shown for more than 200 different materials. The correlation coefficient value equals to 0.99S. Thus in the linear region of a Paris’ curve the crack propagation rate is controlled by the single parameter С or n. The results are presented in tables З, 4 and fig. 4.

As can be seen from the presented analysis the non-direct method for determination of all parameters of the Paris’ curve is developed. The calculated and experimental values of constants C and n are in good agreement.

Table 1

The comparison of results experimental and calculation ЛК/с values

Steels Т, К а02 MPa а ь MPa ЛКі MPa *m (experiment) ARfi MPa *m (calculation) S, %

15KH2MFA 29З 584 700 121.З 127.5 4.8

24З 647 752 59 6З.8 7.5

21З 674 78З 62 72.З 14.2

15KH2NMFA 29З 59З 707 129.4 1З2.8 2.6

24З 658 756 72.46 85.7 15.4

18З 745 94З З4.2 42.9 20.2

AK,h,

MPa*m°'5 30 25 20 15 10 °

0

0,5 1 1,5 2 2,5

CTb/CTy

Fig. 3. The relationship between AKh and ct/ct

Table 2

The comparison of results experimental and calculation AKth values

Steels Т, К 00.2 MPa Ob MPa AKth MPa*m (experiment) AKth MPa*m (calculation) S, %

293 584 700 9.1 10.19 -12

15KH2MFA 243 647 752 12.4 8.85 28

213 674 783 12.5 8.83 29

293 593 707 9.2 9.96 -8.2

15KH2NMFA 243 658 756 10.2 8.36 18

183 745 943 10.6 10.67 -19

St3sp 293 240 470 33.58 30.03 10.58

18Gsp 293 260 500 28.08 28.12 -0.13

09G2S 293 352 503 15.25 15.06 1.24

Fig. 4. The C dependence on a n value

For the lifetime prediction the Wilson’ approach can be used. The number of cycles, N, necessary for crack grows from the initial size a0 to the critical size a can be found from the Paris’

cr

equation as

N = f

da

C(AK)n •

(9)

where Act = ct - ct , M - parameter of

max min r

geometry and the shape of defect, we get

N = f

da

C(AayJMa)n '

(11)

Integrating of the eqn. (11) results in Wilson’ formula:

Assuming that

AK = AayfMa’

(10)

N = -

2

(n - 2)CMn/ 2 Act

a(n-2)/2 a(n-2)/2

u0 ucr

. (12)

a

n

Table 3

The comparison of results experimental and calculation n values

Steels а0.2 MPa аь MPa С (experiment) С (calculation) S, %

20KH13 (1) 655 775 3.12 3.15 1.0

20KH13 (2) 566 749 2.89 3.04 5.1

14KH17N2 782 943 2.56 2.76 7.4

13KH11N2V2MF 885 1 015 2.86 2.88 0.9

08KH17N6T 840 895 2.57 3.18 19.3

1KH16K4NMVFBA 980 1 163 2.56 3.51 27.1

Table 4

The comparison of results experimental and calculation C values

Steels а0.2 MPa аь MPa C (experiment) C (calculation) S, %

20KH13 (1) 655 775 5.89 • 10-9 6.07 • 10-9 2.9

20KH13 (2) 566 749 1.15 • 10-9 1.27 • 10-9 9.4

14KH17N2 782 943 6.71 • 10-9 8.88 • 10-9 24.4

13KH11N2V2MF 885 1 015 3.82 • 10-9 3.79 • 10-9 -0.8

08KH17N6T 840 895 6.04 • 10-9 4.72 • 10-9 -27.9

1KH16K4NMVF BA 980 1 163 1.6 • 10-8 1.99 • 10-8 19.6

The a value is found from the condition of

cr

the pressure vessel fracture or can be taken with consideration of crack size allowed for this structure.

The verification of the suggested model has shown its applicability for express lifetime estimation of different structures.

Conclusions

1. The relationship between AKth and аъ/ау ratio was found. The correlation AKfc(K{c) was also demonstrated.

2. The non-direct method for determination

of ЛХл and and corresponding to them da/

dN values was developed.

3. The method for prediction of Paris’ curve shape through the results of tensile test is suggested. It makes possible to estimate lifetime of different structures with cracks under cyclic loading.

REFERENCES

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МЕТОД ОЦЕНКИ ДОЛГОВЕЧНОСТИ ПО МЕХАНИЧЕСКИМ СВОЙСТВАМ ПРИ РАСТЯЖЕНИИ

Бахрачева Юлия Сагидулловна

Кандидат технических наук, доцент кафедры физики и химии Московского государственного университета путей сообщения (МИИТ), Волгоградский филиал bakhracheva@yandex. ги

ул. им. Милиционера Буханцева, 48, 400120 г. Волгоград, Российская Федерация

Аннотация. Предложен метод прогнозирования формы классической кинетической диаграммы усталостного разрушения по результатам испытаний на растяжение. Для этого разработаны косвенные методы определения пороговых размахов коэффициентов интенсивности напряжений ДКЛ и ДК-, а также соответствующих им значений скоростей da/dN. Установлена взаимосвязь между ДКЛ и отношением предела прочности к пределу текучести ■ Получена корреляция ДК^К^. Показана возможность прогнозирования долговечности различных конструктивных элементов и деталей машин при наличии трещин в условиях циклического нагружения.

Ключевые слова: кинетическая диаграмма усталостного разрушения, циклическое нагружение, долговечность, косвенный метод, испытания на растяжение.