Fracture toughness and resistance determined for large steel structures using stress intensity calculations - fracture mechanic

Wahl, A. M.

English

NASA Technical Reports Server

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NASA INDUSTRIAL APPLICATIONS STUDY 
Industrial Review 
for 
DETERMINATION OF FRACTURE TOUGHNESS PARAMETER 
OF LARGE METAL STRUCTURES 
1 
l Dr. A.M. Wahl I N 6 6  1 3 1 5 6  
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10 ITHRUI IACCESSION NUMBER1 
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Contract NASw 952 9 f f653  July65 
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Presented to 
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 
Office of Technology Utilization 
Washington, D. C . 
bY 
WESTINGHOUSE ELECTRIC CORPORATION 
Defense and Space Center 
Sy s terns Operations 
Baltimore, Maryland 
https://ntrs.nasa.gov/search.jsp?R=19660003867 2020-03-16T21:33:38+00:00Z
8 
NASA INDUSTRIAL APPLICATIONS STUDY 
Industrial Review 
for 
DETERMINATION OF FRACTURE TOUGHNESS PARAMETER 
OF LARGE METAL STRUCTURES 
D r .  A.M. Wahl 
10 December 1964 
Contract NASw 952 
Presented to 
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 
Office of Technology Utilization 
Washington, D. C. 
by 
WESTINGHOUSE ELECTRIC CORPORATION 
Defense and Space Center 
Systems Operations 
Baltimore, Maryland 
c 
CONTENTS 
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . .  
CONTRIBUTIONS O F  NASA TECHNICAL NOTES D-2395 
ANDD-2206 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  
POTENTIAL APPLICATION OF METHOD DEVELOPED 
IN TECHNICAL NOTE D-2395 . . . . . . . . . . . . . . . . . . . . . . . . .. 
P O T E N T I A L F U R T H E R D E V E L O P M E N T S . . . . . . . . . . . . . . . . .  
CONCLUSIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  
FIGURE 
1 Manjoine Specimen Schematic . . . . . . . . . . . . . . . . . . . . . . 
Page 
1 
3 
5 
7 
9 
10 
5 
ii 
INTRODUCTION 
A tremendous amount of research  i s  now being conducted on the subject of 
This involves the determination f rac ture  mechanics and f rac ture  toughness. 
of the f rac ture  or  bursting strength of la rge  s t ruc tures  or machine components 
which may have small cracks or  defects present .  
to industry include, for example, l a rge  turbine or  generator ro to r s ,  turbine 
disks ,  p re s su re  vessels  of va r ious  types,  large blowers and fans ,  l a rge  oil 
tanks,  and railway axles.  
or may develop after a t ime from fatigue or repeated loading af ter  which the 
s t ruc ture  may fail catastrophically, often with large losses  of life and prop- 
e r ty .  
a s t ructure  becomes tremendously important, but a t  the same t ime it may be 
extremely difficult. 
Such s t ruc tures  of in te res t  
Small c racks  may be present  in such s t ruc tures  
For  this reason,  the problem of predicting the f rac ture  strength of such 
One approach to this problem which is  coming into wide use  i s  the f rac ture  
.b -8-
mechanics approach a s  discussed in  reference 1 . In this approach, the 
elast ic  s t r e s s  is calculated i n  the immediate neighborhood of a c rack  in a 
s t ructure .  
intensity factor.  This parameter depends on the shape of the s t ruc ture  and 
on the load; however, it  i s  not the same  a s  a s t r e s s  concentration factor.  It 
is postulated that a t  some critical value of K for  a given mater ia l  (denoted by 
K ) rapid c rack  propagation and complete o r  catastrophic fa i lure  will  occur. 
This value of K 
values of K 
conditions occur) and these values a r e  called K 
t u r e s ,  we a r e  concerned with the plane s t ra in  f rac ture  toughness K 
:iC References a r e  listed at  the end of this review 
This s t r e s s  is characterized by a parameter  K called the " s t r e s s  
1 C 
is frequently called f rac ture  toughness. Usually the lowest 
C 
a r e  obtained for relatively thick specimens (where plane s t ra in  
In most  pract ical  s t ruc-  
C 
I C '  
values.  
I C  
Using this f r ac tu re  mechanics approach, the problem of predicting the 
bursting o r  f r ac tu re  s t rength of a s t ruc ture  reduces to: (1) calculating the 
K-value for  the actual s t ruc ture  under operating conditions, and (2)  de t e r -  
mining the K 
The contribution of NASA Technical Note D-2395 
-value f o r  the given mater ia l  by u s e  of a suitable tes t  specimen. 
is largely in the la t te r  phase 
2 I C  
. 
2 
CONTRIBUTIONS O F  NASA TECHNICAL NOTES 
D-2395 AND D-2206 
fo r  any mater ia l  a r e  found by ten- 
KC , Normally, s t r e s s  intensity factors,  
sion tes t s  on specimens having sharp notches or  c racks .  These specimens 
may be flat bars  with c racks  on two opposite s ides  or  round bars  containing 
deep notches. 
wel l  known; however, t o  find the plane s t ra in  values (K 
it is necessary  to go to  extremely large s ize  specimens,  which unfortunately 
require  extremely high load capacity tensile testing machines. 
are  not normally available. 
The formulas for  calculating K-values for such specimens a r e  
) for many mater ia l s ,  
I C  
Such machines 
To avoid such high load requirements,  tensile specimens made of flat plates 
with a notch on one side (the single-edge-notch tension specimen) a r e  now being 
used. Such specimens require  much lower capacity testing machines; how- 
eve r ,  the determination of the cri t ical  s t r e s s  intensity factors ,  K or  K , 
f r o m  such specimens has been rather  uncertain since no formulas w e r e  
available for  calculating K-values for such specimens.  
C I C  
2 
finding the K-factors for  such single-edge-notch tension specimens,  a s  well  
as for  other shapes of specimens. These K-factors  a r e  found a s  a function 
of ra t io  of notch depth to width of specimen, and a l so  the rat io  of specimen 
length t o  width. 
procedure applied to  the well-known Williams s t r e s s  function. 
that  the first matr ix  coefficient is proportional to  the s t r e s s  intensity factor 
K. 
geometr ical  proportions. 
The contribution of TN D-2395 consists of the development of a method fo r  
Technically, the method uti l izes a boundary value calculation 
It tu rns  out 
Thus, the method is useful for  finding K-values for specimens of different 
The theoretical  resul ts  of TN D-2395 were  checked by an experimental  corn- 
3 
pliance procedure in TN D-2395. 
of the method. 
This offers fur ther  proof of the validity 
3 
The procedure developed in TN D-2395 should be of value in the fur ther  de- 
velopment of f r ac tu re  mechanics since the method may well  be applied not 
only to the single-edge-notch tension specimen but a l so  to  other shapes of 
specimen which have fur ther  possibilities, as  discussed la te r .  Thus, the 
method should be valuable to  industry in general ,  since it would contribute 
toward better es t imates  of bursting strength or  f r ac tu re  s t rength of s t ruc -  
t u re s ,  p re s su re  vessels ,  or machine components. 
4 In TN D-2206, a pract ical  method was developed fo r  analyzing plastic 
deformations in  biaxial s t r e s s  fields or  plate type s t ruc tures .  
appears  promising for analyzing plastic s t ra ins  in t e s t  specimens such as the 
single-edge-notch tension specimen considered in reference 2 .  
discussion of this in a la ter  paragraph. ) 
This method 
(See further 
4 
POTENTIAL APPLICATION O F  METHOD DEVELOPED 
IN TECHNICAL NOTE D-2395 
5 
Recently, a shape of specimen developed by Manjoine has  been utilized 
for  determining plane s t ra in  f rac ture  toughness K -values. This specimen 
has  advantages of s m a l l  s ize  and a high degree  of constraint .  
which indicates schematically the method of load application. ) 
I C  
(See f igure 1 
Commonly used 
dimensions a r e  AB = 0 . 5  inch and BC = 1.6 inches. 
important i n  experiments involving neutron i r rad ia t ion  where  it is des i red  t o  
determine f r ac tu re  toughness of l a rge  p r e s s u r e  vesse ls  utilized in nuclear  
power plants. 
u e s  for  different ra t ios  of c rack  length t o  width, a/w, and of different ra t ios  
These advantages a r e  
However, the question a r i s e s  a s  t o  how t o  calculate the K-val-  
of v/w. 
B C 
1951 -VA-2 
Figure  1. Manjoine Specimen Schematic 
2 
The method developed in  TN D-2395 is valuable in that it may be applied 
t o  the specimen of figure 1 ,  which is loaded differently f r o m  the single-edge- 
notch tension specimeii of reference 2; 
spec imen is actually loaded by a pin on the upper half and through a bolt 
As indicated in  re ference  5,  this  
5 
threaded into the lower half. 
u r e  1 will be sufficiently c lose for  an analytical  approach. 
It i s  expected that  the schematic  loa1 ig-  
In applying the method of reference 2 t o  the specimen of figure 1,  a uniform 
shea r  s t r e s s  and ze ro  no rma l  s t r e s s  a r e  assumed along the edge AB as shown. 
Z e r o  shear  and normal  s t r e s s e s  a r e  a l so  assumed along edges BC and CD. 
Using the s a m e  s t r e s s  function as  assumed in re ference  2 and utilizing the 
boundary conditions of figure 1,  the values of s t r e s s  intensity factor  K may 
be found for  various rat ios  of v/w and a/w. 
mation on the effects of varying dimensions in this specimen. 
This would provide useful infor- 
6 
POTENTIAL FURTHER DEVELOPMENTS 
The method of TN D-2395 should also be of value in estimating the s ize  of 
It is  believed that the s ize  the plastic region near  the c rack  tip 0 of f igure 1 .  
of this plastic zone should be kept small compared t o  the thickness of the 
specimen (perpendicular to  the x-y plane of figure 1) in order  f o r  this approach 
(utilizing the K -factors) to be valid. 
I C  
Technically, the plastic zone size could be estimated approximately a s  
1 
follows utilizing the s t r e s s e s  calculated using the method of TN D-2395. 
this  case,  the assumption is made that the axial  s t ra in  is zero,  and f r o m  this  
condition the axial  s t r e s s e s  could be calculated a t  any point using known 
elasticity equations. 
an equivalent s t r e s s  using the maximum shear  o r  octahedral shear  strength 
theory. 
the plastic zone could be estimated. 
of the required specimen thickness. 
In 
These s t r e s s  components could be combined to  give 
Knowing this  s t r e s s  and the yield s t r e s s  of the mater ia l ,  the s ize  of 
This would be useful in obtaining an idea 
The same  general  method might be applied to  obtain an idea of the plastic 
zone s ize  for the single-edge-notch tension specimen discussed in reference 2 .  
The method for analyzing plastic s t r e s s e s  and s t ra ins  given in TN D-2206 
4 
a l so  appears  t o  be of potential value in evaluating the resul ts  obtained f r o m  
f r a c t u r e  tes t s  on various shapes of specimen such a s  the single-edge-notch 
tension specimen of reference 2 o r  the shape shown in figure 1. The use  of 
such a method would be of particular value in evaluating cases  where the 
plastic zone s ize  is relatively large. This would be a contribution to  the 
fur ther  development of fracture mechanics. It appears  that the method could 
be applied not only t o  the tes t  specimens considered in references 2 and 5, 
but a l so  to  other cases  commonly used s u c h  2 s  the double-edge-notch-tension - 
specimen. 
7 
In T N  D-2206,  the equations were given for  a plane s t r e s s  condition s o  that 
they apply s t r ic t ly  only to  thin plates; however, it i s  believed that these equa- 
tions may be modified to  apply to  plane s t ra in  conditions which a r e  of g rea t  
pract ical  interest  to  industry. 
One further development which would be of value i s  t o  utilize the s t r e s s  and 
s t r a in  distributions obtained using the method of T N  D-2395 as a start ing point 
for the i teration method of T N  D-2206. 
number of i terations required to  obtain a solution for  a given loading. 
This may be helpful in reducing the 
Actual tes t s  on different materials to  cor re la te  the resu l t s  obtained on 
specimens of different geometries should a l so  be made as a check on the 
analytical resul ts .  
a 
CONCLUSIONS 
The subject of f rac ture  mechanics is a rapidly developing field which is of 
great  pract ical  importance to  a number of industr ies ,  particularly where large 
s t ruc tures  or machine components subject t o  high s t r e s s e s  a r e  concerned. 
Such industries include the electrical ,  heavy machinery,  oil, s teel ,  and 
chemical industries.  
mentioned: turbine and generator ro tors ,  turbine disks ,  l a rge  blowers and 
fans,  p re s su re  vessels  of various types,  and oil tanks. It is important t o  
design such s t ruc tures  s o  that catastrophic failure will not occur and a t  p re s -  
ent the f rac ture  mechanics approach is most  widely used. 
Among the s t ruc tures  involved the following may be 
The contribution of NASA TN D-2395 is valuable to  industry in that it 
provides a practical  method of calculating the f r ac tu re  toughness parameter  
for  a variety of t e s t  specimen shapes. 
calculation of f racture  strengths in  a variety of shapes of actual s t ruc tures  
or  machine components. 
These can la te r  be applied to  the 
The contribution of NASA TN D-2206 consists in the development of a 
method for  analyzing plastic strains in plate type s t ruc tures .  
method appears  t o  be valuable for the fur ther  development of the f rac ture  
mechanics approach, particularly for  cases  where considerable plastic flow 
m a y  occur before f rac ture .  
This general  
9 
REFERENCES 
1. Report  of ASTM Special Committee on F r a c t u r e  Testing-----  , Materials  
Research  and Standards,  March 1964, p. 107. 
2 .  NASA Technical Note D-2395, B. Gross ,  J. Srawley, and W. F. Brown, 
J r .  , "Stress  Intensity Fac tors  for  a Single-Edge-Notch Tension Specimen 
by Boundary Collocation of a S t r e s s  Function. 
3. NASA Technical Note D-2396, 3. E .  Srawley, M. H. Jones,  and B. Gross ,  
"Experimental  Determination of the Dependence of C r a c k  Extension F o r c e  
on Crack  Length for  a Single-Edge-Notch Tension Specimen, August 1964. 
4. NASA Technical Note D-2206, E. Roberts ,  Jr .  and A. Mendelson, 
"Analysis of P las t ic  Thermal  S t r e s ses  and Strains  in a Finite Thin P la te  
of Strain Hardening Mater ia l ,  I t  1964. 
5. M. J. Manjoine, "Biaxial Brit t le F r a c t u r e  T e s t s , "  paper presented at the 
AWS-ASME Metals Engrg. Conference, Detroit ,  May 1964. 
10 


Determination of fracture toughness parameter of large metal structures Industrial review

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