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Thermal Fatigue
Analytical Model of Solder Shear Fatigue [2]
 The fatigue life of the solder joint is determined by the amount of accumulated fatigue
damage. When the accumulated fatigue damage exceeds the capability of the solder joint
failure occurs.
 A solder joint response can be characterized by a hysteresis loop in the shear stress-strain
plane (figure 3 pg743 [2]). The area of the hysteresis loop represents the viscoplastic strain
energy density per cycle W. The hysteresis loop is limited by a constant stress envelope,
independent of thermal expansion mismatch, determined by the solder yield strength during
initial elastic loading and plastic yielding, and the stress reduction lines during creep and
stress relaxation. The maximum strains, , are determined by displacement caused by
thermal expansion mismatch.
 J.D. Morrow has proposed a generalized fatigue damage law on the basis of cumulative
stored viscoplastic strain energy density (eq. 1,2 pg743 [2])
1  W 
Nf  

2  Wf 
1
C
1   p 
Nf  

2  f 
1
C
Nf  shear fatigue life
Wf  material constant
C  constant between -0.5 to -0.7 for metals
γ p  applied plastic strain range

For a leadless chip resistor which has very stiff leads the above equation can be written as:
(eq. 3 pg744 [2])
1
1    C
Nf  

2  2f 
 For solder creep and stress relaxation is significant relative to the initial plastic strains due to
yielding, determination of W or p is not straightforward. The total plastic strains increase
with time as the strain energy elastically stored in the assembly (component, solder joint,
PCB) is converted to irreversible viscoplastic strain energy in the solder that is subject to
creep and stress relaxation. For solder over time-temperature operation virtually all of the
elastically stored strain energy will convert to irreversible viscoplastic strain energy in the
solder.
 To overcome the difficulty of determining the time and temperature dependent plastic shearstrain range p the maximum available displacement shear and accounting for the incomplete degree of stress relaxation or creep with a time-temperature dependent exponent. The
total cyclic strain range is given by (eq 6,7,8,9,10,11, pg744 [2])
1
LD
  T 
h
Δ  αΔT  = thermal expansion mismatch
  f
  T   STS  CTC
Simplifying the right side eq XX becomes
  T   c Tc  STS  CTC
and
S TS   C TC

If there is no power being dissipated by the device
Tc 
Tc  TS
And the max distance between solder joints (LD) is approximately
1 2
LD 
L  W2
2
2
Discussion on Fracture and Crack Growth
[11]
Fatigue failures occur in solder joints due to cyclic loads and repeated reversal bending. Failures
in materials arise from crack initiation and propagating under these cyclic loads. These fatigue
failures can be thought of a process of crack initiation and propagation. In any material including solder there will be initiation sites. If the applied loads are small the strength of the material
is not affected. At higher loads irreversible changes in the material takes place and a fatigue
fracture will initiate at a discontinuity or other stress riser in the material. Once the fracture is
initiated it will grow or propagate until the cross section is reduced until it can no longer support
the loading and then the material will crack. In practical applications vibration, thermal shock
and mechanical shock are possible the primary failure mechanism of concern in a surface mount
solder joint is cyclic differential thermal expansion. [2]
Cracks that develop in Sn63Pb37 eutectic solder joints exposed to thermal cycling are intergranualar, which is the cracks propagate along the grain boundaries that separate the Sn rich and
Pb rich phases. The crack growth mechanism at high homologous temperature and low cycle
frequency has been suggested to be nucleation, growth, and coalescence of cavities along the
grain boundaries.
During thermal cycling creep couples with the fatigue mechanism such that the creep crack
growth is enhanced by the fatigue mechanism. High temperature fatigue tests on eutectic solder
concluded that fatigue resulted in the development of cavities in the as-cast and superplastic
eutectic alloy. The cavitations occurred at the intercolony boundaries of the as-cast material
(grain size = 50-80 m) and between the separate the Sn rich and Pb rich phases in the superplastic eutectic (grain size = 5.8 m). Once the initial crack is formed by one of the above
mechanism the crack will propagate under the applied stress until fracture occurs.
Numerically, fatigue crack growth for the solder can be described by the J (elastic-plastic)
integral and C* (creep) integral [solder mechanics] where the J-integral controls crack growth
and the C*- integral controls the creep part. See figure Xx)
3
 C 

 ij  
BI
r
 n 
 C 

 ij  
 BI n r 
1
n
 n 1
 n 1
1
 m 1
~ 

ij
 J 

 ij  
x

I
r
m 

~ 
ij
 J 

 ij  x
 xI n r 
4
m

 ij 
 m 1

 ij 