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Al-Khwarizmi 

Engineering   
Journal 

 
Al-Khwarizmi Engineering Journal, Vol. 14, No. 4, December , (2018) 

P.P. 9- 15 

 
Crack Growth Behavior through Wall Pipes under Impact Load and 

Hygrothremal Environment 
 

Ali Jamal Khaled*             Ahmed Abdul Hussain** 
*,**Department of Mechanical Engineering/ College of Engineering/ University of Baghdad  

*Email: engalijamal93@gmail.com 
**Email: ahmedrobot65@yahoo.com 

 
(Received 12 February 2018; accepted 14 May 2018) 

https://doi.org/10.22153/kej.2018.05.001 

 
Abstract 

 
This research concerns study the crack growth in the wall of pipes made of low carbon steel under the impact load and 

using the effect of hygrothermal (rate of moisture 50% and 50℃ temperature). The environmental conditions were controlled 
using high accuracy digital control with sensors. The pipe have a crack already. The test was performed and on two type of 

specimens, one have length of 100cm and other have length 50cm. The results were, when the humidity was applied to the 

pipe, the crack would enhance to growth (i.e. the number of cycles needed to growth the crack will reduce). In addition, 

when the temperature was increase the number of cycles needed to growth the crack are reduced because the effect of heat 

on the mechanical properties of the material. In addition, when the test performed on the specimens of length 50cm the 

number of cycles needed to growth the crack is increase because the effect of bending stress on the pipes. 

 
Keywords: Cracks, crack initiation, crack growth, hygyothermal, pipes failure. 

 
1. Introduction 

 
Cracks define as a discontinuity or break which 

occur in solid (rigid) body and it branded by having 

an initiation point and by growing from this point 

to finite size with time. Either leading or not to the 

separation the original body in two or more parts. 

Crack growth depended on the loading conditions 

and environmental conditions. Loading conditions 

presents the type of load such as static load, 

dynamic load, load controlled, grip controlled. 

While Environmental conditions like temperature 

and corrosive atmosphere influence crack growth. 

[1]  
There are three types of cracks in pipe happen 

due to several causes associated with their types; 

first the form of a crack, second its dimension and 

its function. [2] 

1. Longitudinal cracks  
2. Lateral cracks 
3. Cracks origination at a point 

 
2. The Behavior of Cracks 
 
The behavior of fatigue cracks differs from that 

of long cracks because of larger sensitivity to the 

microstructure. A greater size of the plastic zone fit 

to the crack length, and a minimum fit to crack 

finish. Advanced have been made in the 

understanding of the fatigue crack growth process 

of cracks, and this understanding has been 

employed in the advance of analytical treatments 

of short fatigue crack growth. The study of fatigue 

crack growth behavior is one of the more active 

areas of research in the field of fatigue. Such cracks 

are interest not only because their growth can 

inhabit an important portion of the fatigue life time 

but also because they can grow at amount much 

higher or lower than might be expected on the basis 

on long crack behavior. There are four kinds of 

cracks fatigue [3] 

1. Mechanically cracks (the crack length is less 
than plastic zone size) 


Ali Jamal Khaled                                Al-Khwarizmi Engineering Journal, Vol. 14, No. 4, P.P. 9- 15 (2018) 

10 

 
2. Micro structurally (the crack length is less than 
a critical microstructural) 

3. Physically (the crack length is less than at which 
crack closure if fully developed usually less 

than 1 mm in length)  

4. Chemically (the crack length may be up to 10 
mm) 

 
3. Governing Differential Equations 
 
Paris proposed the following equation for the 

correct crack propagation law 
��
�� =  ∁(∆	)�                                                … (1) 
Where ∁ and � are constant and they depended on 
the material that be used. 

This equation seemed to have good correlation 

with the test data. However, if comparisons are 

made with the large range of data, such as a higher 

load ratios and crack growth rates, the correlations 

is not good. In fact, equation (1) does not seem to 

be complete. Two effect occur which are not taken 

into account. One of this variation in the crack 

growth rate owing to the load ratio, R. the other is 

the instability of the crack growth when the value 

of the maximum stress intensity factor approaches 

to the fracture toughness of the material, Kc, [4] 

 
4. Criteria of Crack Growth 
 
Theoretical and experimental work contains 

different criteria like crack position, shape of crack, 

length of crack and crack angle. Moreover, 

approximation for the study of the crack growing 

path. Several of this study are created on the stress 

analysis of the crack tip region. Erdogan and Sih 

first examined the angled crack. They suggested 

the MTS criteria basing the stress domain present 

just before the start of break for guess of the 

orientation of the initial crack growth. Conferring 

to the MTS criteria the crack extend in the radial 

way agreeing to the tangential stress and the crack 

growth occur then this maximum arrive a ticklish 

value. Erdogan and Sih’s study was created on the 

presentation of the crack tip stress region in 

expressions of stress function resulting by 

Williams [5]. 

∅=��/��� (θ)+�� �� (�)+��/� �� (�)      ...         (2) For the first term the stress are 
representation by: 
)* =  �√�,-. cos

�
�  � 0	� 123�  

*
� −  	� 356�7 … (3)  

8-* =  ��√�,-  123
�
� � [	� 356� + 	�(3123� − 1)  

                                                                       … (4) 

Erdogan and Sih suggested that the direction of 

crack growth is given by the condition: 
�<=
�* = 0                                                            … (5) 
Where: 

	* =  123� *�  (	�123
*
� − 3	�356

*
�)               … (6) 

123 *� [	? 356� + 	?? (3123� − 1)]=0              … (7) 
     A better covenant among the theoretical and 

experimental has been gotten by a personification 

of the stress region using the first two relations of 

the Eigen function, equation (2). In addition, by 

using a lesser but finite radius to detect the 

maximum assessment of )* and this was exposed 
by Williams and Ewing. The elastic strain energy 

AB kept in parallel pipe of volume AC in the 
dominate Sih expresses region of the strained plate: 
�D
�E =  

�FG
HI  [	�,�K)L + )M N

� +  K)L − )M N� +
4(8LM )�]                                                          … (8) 
	� =  �PG�FG         For plane stress                       … (9) 	� =  1 − 2Q   For plane strain                     … (10) 

Papadopoulos used the elastic strain energy 

approached to suggest a standard of break, which 

takings into account the third stress constant Det. 

(σij) 

Det.K)RS N =  T
)L )LM)ML )M T                             … (11) 

Where: 

)ML = )LM 
Conferring to the Det. – criteria the position of 

crack growth for the mixed mode loading is 

specified from the state that the determinate of the 

stress tensor necessity take a maximum rate. In a 

polar coordinate system, the relations express these 

conditions mathematically: 
U VWX.(Z[\)

U* T*]*∗ = 0,  
U. VWX.(Z[\)

U*. T*]*.  < 0       … (12) 
The ticklish stress for crack initiation is 

estimated by: 

Det.()RS) = Det.()RS )`-                                    … (13) 
 

5. Cyclic Load Equations 
 

The equations below are available for 

transverse crack (α = 90°) with and without internal 
pulse pressure [6] 

c = d[1 + e�F�fIghi ]                                         … (14) 
j =  ,kH  (lmH − jmH)                                    … (15) 
n =  iopHqI?     (For simply supported)              … (16) 
σ =  stu       (Bending stress)                          … (17) σvwx = −σvyz                                            … (18) 


Ali Jamal Khaled                                Al-Khwarizmi Engineering Journal, Vol. 14, No. 4, P.P. 9- 15 (2018) 

11 

 
{ = �\-                                                           … (19)    
|} = �\√-X                                              … (20)  ~�(|}) = 1 + 0.19|} + 0.01|}�                   … (21)  
�� = 1 + }.�}��(�P�`�X(�))0���(���)√. F√� ���(�)7∗�

                    … (22)   

�� = 1 + }.�����K�F�`�X
.(�)P`�X(�)N

0���(���)√. F���(�)7
           … (23) 

 ���? = (~�(|}) ∗ �56({) ∗ ��)/({ ∗ ��)  …(24) 
�? = )�pp.���S ���? = �?��L                   … (25) 
 

6. Material Used and Specimens 
 

The material used in this research is Low 

Carbon Steel (EN 10219 S235JRH). It is a pipe 

with a circular section thickness about 1.4 mm and 

a diameter about 75 mm. This research was done 

on several samples of this article. Some of these 

samples have a length of 100 cm [7], See Fig. 1 and 

other have length of 50cm See Fig. 2. The reason 

for this difference to test the effect of bending on 

the growth and behavior of the crack. This test was 

conducted under different environmental 

conditions to determine the effect of the moisture 

and heat factors on the growth of the crack. 

 
Fig.1. Two sample of length 100cm. 

 
Fig. 2. Two sample of length 50cm. 

7. Manufacturing of The Rig 
 

This device was made of several parts of iron 

material with different sections according to the 

required part. Also used the technique of electric 

arc welding to connect these parts. The parts are cut 

using the cutting machine. After the cutting, the 

welding process is carried out to connect them 

together. However, most parts of this machine have 

the ability to switch when failure or damage occurs 

in one of these parts. The rig has the facility of 

making test for different length of pipes and 

different fixing conditions to match the 

requirement for the end fixing. A wooden plate was 

used to fix the parts of the machine. The 

dimensions of this plate are (122 cm x 244 cm) and 

thickness 1.5 cm. This plate has a hole in the 

middle to facilitate the passage of the hammer lever 

and to facilitate the examination of the pipe using 

the camera or naked eye. The dimensions of the 

parts of each other were developed using a laser 

device called (level) (see fig.3) that allows the 

device to see the extent of the separation of these 

parts or deviation from each other, which adds the 

possibility of placing the parts with high accuracy. 

This device enables the possibility of conducting 

tests on pipes made of iron, carbon steel, 

aluminum, copper and plastic. The design of this 

device includes the possibility of changing the 

height of the hammer to suit the amount of energy 

necessary and strong with the ability of the metal 

to withstand the shocks, Also can work on the pipes 

of different length ranging from 50 cm to 150 cm 

and different diameters ranging from 2 to 4 inch.   
In addition, the researcher or worker on this device 

can control the environmental conditions to be 

operated from heat, humidity, and control where it 

can work in the areas of temperature ranging from 

0 °C to 100 °C. Also, control the humidity, where 

it can work in the humidity ratio ranging from 0% 

to 100%. 

 
Fig. 3. level device. 


Ali Jamal Khaled                                Al-Khwarizmi Engineering Journal, Vol. 14, No. 4, P.P. 9- 15 (2018) 

12 

 
8. Material Properties 
 

These properties from DIN EN 10219 

1. Chemical composition 
     Chemical composition is in percentage by mass. 

See Table 1. 

2. Mechanical properties 
    These mechanical properties measured at room 

temperature, See Table 2 

3. Physical properties. 

 Physical properties for this material shown in the 

Table 3. 

Table 1, 

Chemical properties of material 

Carbon   C Silicon    Si Manganese  Mg Phosphorus  P Sulfur  Ag Nitrogen  N 

0.17 - 1.4 0.04 0.04 0.009 

 
Table 2, 

Mechanical properties of material 

Yield strength in N/mm2 min for nominal wall thickness 235 

Tensile strength in N/mm2 for nominal wall thickness 360-510 

Elongation % for nominal wall thickness 24 

Impact energy in J at temperature 20°C 27 
 
Table 3, 

Physical properties of material 

Density at 20°C in kg/dm3 7.85 
Modulus of elasticity kN/mm2 at 20°C 210 
Thermal conductivity at 20°C in    w/ m k 54 
Spec. thermal capacity at 20°C   J/kg k 461 
Spec. electrical resistivity at 20°C     Ω mm²/m 0.15 

 
9. Crack Initiation 
 

The crack was created manually by handsaw. 

Because that the crack is difficult to accomplish 

using other machines. Where the length of the cut 

about 24% [8] of the perimeter of the pipe. This 

percentage was based on previous research, where 

the length was 56 mm and width of the crack is 

about 0.7 mm to 0.9 mm. This difference is due to 

the difference in the thickness of the cutting edge 

in the saw as well as the hand movement. Other 

percentages were chosen to indicate the possibility 

of conducting the search on different lengths of the 

crack. However, these lengths of (18mm, 25mm, 

30mm, and 40mm) took a long time without any 

continuity in the growth of the crack. 

 
10. Results and Calculations 
 

Table 4. and table 5. Show the calculations that 

must be used in this search, then use it in the 

governing equations, table 6 and table 7. To ensure 

the regular work convicted by equations in point 5. 

Results were obtained by using rig made for testing 

these specimens. See Fig. 4, the tests were repeated 

again to ensure a close test result as well as to 

ensure the correct functioning of the rig. The 

results are shown in the Fig. 8, Fig. 9, Fig. 10, and 

Fig. 11. 

Outer diameter (OD) =0.075m, inner diameter (ID) 

=0.0722m, thickness (t) = 0.0014m      Yield point= 

235 Mpa, modules of elasticity (E) = 210Gpa, high 

(h) =0.57m, weight of hammer (w) = 6.7Kg  

Table 4, 

Calculation for 100cm specimens. 

Effective length is 1 m 

Load applied N Moment of inertia   �� Deflection  � Bending stress  Mpa 
2279.3  0.22 ∗ 10Pk  0.0103  1949.1  

 
Table 5, 

Calculations for 50cm specimens 

Effective length is 0.5 m 

Load applied   N Moment of inertia    �� Deflection   � Bending stress   Mpa 
2223.2  0.22 ∗ 10Pk  0.0018  1378.1  

 
Ali Jamal Khaled                                Al-Khwarizmi Engineering Journal, Vol. 14, No. 4, P.P. 9- 15 (2018) 

13 

 
Table 6, 

Calculation using cyclic load equations for 100cm specimens 

Type of test k1 k2 Slop (�) 
without LHS RHS LHS RHS LHS RHS 

1.8*10q 1.8*10q 1.87*10q 1.87*10q 6.91 8.4 
hygrothermal 1.3*10� 1.3*10� 1.34*10� 1.38*10� 6.02 2.4 

 
Table 7, 

Calculation using cyclic load equations for 50cm specimens 

Type of test k1 k2 Slop (�) 
without LHS RHS LHS RHS LHS RHS 

1.33*10q 1.33*10q 1.35*10q 1.35*10q 2 7.6 
hygrothermal 9.22*10q 9.5*10q 9.28*10q 9.7*10q 3.9 7 

 
Fig. 4. The rig used in this research. 

 
Fig. 5. Humidifier device. 

 
Fig. 6. Support.  

Fig.7. Close up photo show the crack and crack 

growth. 

 
Fig. 8. Show number of cycle of 100cm specimens. 

 
Fig. 9. Show number of cycle of 50cm specimen. 

 
Hamme

Chamber 

Support 


Ali Jamal Khaled                                Al-Khwarizmi Engineering Journal, Vol. 14, No. 4, P.P. 9- 15 (2018) 

14 

 
Fig. 10. Effect of hygrothermal on crack growth 

for 100cm specimens. 

 
Fig.11. Effect of hygrothermal on crack growth for 

50cm specimens. 

 
11. Conclusion 
 

The purpose of this study is to determine the 

extent to which the crack is able to grow when 

shedding and how long it takes to grow these 

cracks. Some things need to be discussed to 

know what changes are made to these cracks and 

to make things better. 

1- The number of cycle needed to growth the 
crack are reduced due to the effect of 

humidity because the formation of oxides on 

the fracture surface. 

2- The number of cycle needed to growth the 
crack in the specimens of length 50cm are 

increase because the effect of bending stress 

in the pipes. 

3- The number of cycles needed to growth the 
crack are reduced because the effect of heat 

on the mechanical properties of the material 

that helps to increase the ductility. 

 
Notations  
 

LEFM        linear elastic fracture mechanics 

MTS           multi-tasking staff 

da/dN         crack growth per cycle, m/cycle 

r,θ              polar coordinate, dimensionless 
k1 , k2                stress intensity factor, Mpa√� 
�                young modulus, Gpa 
 

Greek Letters 
 

π mathematical constant, 
dimensionless 

Q poison ratio, dimensionless 
n deflection, m 
� angle of crack propagation, degree 
8-* shear stress in cylindrical 

coordinate, Mpa 
)L  , )M  
 , 8LM 

component of stress tensor, Mpa 

 
)* circumferential stress near crack 

tip, Mpa 

{ non dimensional factor, unit less 
 
12. References 

 
[1] Bertram Broberg, K., 1999, Cracks and 

Fracture Academic press, pages 1-4, ISBN: 

978-0-12-134130-5 

[2] Stein, D., 2004, Rehabilitation and 
Maintenance of Drains and Sewers, 

technique technology center 

[3] Mcevily, A. J, 1996, The Growth of Short 
Fatigue Crack, Transaction of material 

science, Vol. 13, pages 1-5 

[4] Forman, R. G., Kearney, V. E., Engle, R. M., 
1967, Numerical Analysis of Crack 

Propagation in Cyclic Loaded Structures, 

pages 459-463 

[5] Wasiluk, B., Golos, K., 2000, Prediction of 
Crack Growth Direction under Plane Stress 

for Mixed Mode I and II Loading, pages 6 

[6] Al Laham S., Ainsworth R. A.,1999, Stress 
Intensity Factor and Limit Load Handbook, 

British Energy Generation Ltd., UK  

[7] Anil, O., Erdem, R. T., Kantar, E., 2015, 
Improving the Impact Behavior of Pipes 

Using Geofoam Layer for Protection, 

International Journal of Pressure vessel and 

piping, pages 52-64 

[8] G. M. Wilkowski, Gadiali, N., Rudland, D., 
Krishanswamy, P., Rahman, S., Scott, P., 

1994, Short Cracks in Piping and Pipe Welds, 

Vol 4, no 1, pages 78 
 

 )2018( 9- 15، صفحة 4د، العد14دجلة الخوارزمي الهندسية المجلم                                                                   علي جمال خالد

15 

 
 نمو الصدوع وتصرفها خالل جدران االنابيب المعرضة ألحمال صدمية ومحيط حار ورطب
 

  **ناحمد عبد الحسي             *    علي جمال خالد
 كلية الهندسة / جامعة بغداد قسم الهندسة الميكانيكية/*،**

  gmail.com93alengalijam@: يالبريد اإللكترون*
  yahoo.com65ahmedrobot@البريد االلكتروني: **

  
  الخالصة
  

 ٥٠الحرارة (يتناول هذا البحث دراسة نمو الصدع في جدار االنابيب المصنوعة من الفوالذ منخفض الكربون تحت تأثير حمل الصدمة واستخدام تأثير 
وي على صدع . تم التحكم في الظروف البيئية باستخدام جهاز تحكم عالي الدقة مع أجهزة االستشعار. االنابيب تحت)%٥٠( بنسبة الرطوبةمئوية) ودرجة 
ق الرطوبة سم. عند اجراء االختبار فأن النتائج كانت، عند تطبي٥٠سم واألخر ذو طول ١٠٠ذو طول  على نوعين من النماذج أحدهااالختبار اجري و مسبق،

الشق سوف يقل بسبب تأثير درجة الحرارة على  نموكذلك عند تطبيق الحرارة فأن عدد الدورات الالزم ل فأن عدد الدورات الالزمة لنمو الصدع سوف تقل.
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