Spotweld (Bolt or Adhesive Connection)

There are three different ways of modeling spotwelds:

Nodal connection
Spring (/PROP/TYPE13) connection
Solid connection

Spring (/PROP/TYPE13) connection and solid connection may also be used to model a bolted or adhesive connection (glue).

Nodal Connection

A single interface TYPE2 with the first surface as the main side and some nodes from the second surface as secondary nodes: With this solution the mesh of the main surface can be independent of the spotweld location. Hourglass problems disappear on the main surface. On the second shell, the surface mesh must respect the spotweld location and the hourglass problem will remain. The main problem with this modeling approach is the undeformability of the connection and its infinite strength.

Spring (/PROP/TYPE13) Connection

Two tied interfaces and a spring: The use of two tied interfaces will provide a full symmetrical solution allowing a free mesh on the two surfaces and avoiding hourglass. The spotweld is modeled with a beam type spring element. The spring element uses independent nodes not connected directed to the shell elements. One of the two nodes is located on the first surface (or near to it, there is no need to be located exactly on the shell surface) and the second node is located on the second surface. One tied interface connects one spring node with the first surface and a second tied interface does the same for the second node on the second surface.

To create a spotweld using this method is a good alternative solution with this approach the connection location is independent from the shell mesh. It is more accurate than the above node connection modeling, since the spotweld properties are input directly for the spring TYPE13.

Moreover, there are two different ways to model rupture of the spotweld:

Use failure criteria which are available for a spring TYPE13. For more details, see the comments for failure criteria in /PROP/TYPE13 (SPR_BEAM).
Use Spot_flag= 20, 21, or 22 in the Tied Contact (Tied Contact (/INTER/TYPE2)).
Note: The spring TYPE13 modeling technique for spotwelds can also be used for other kinds of connections such as welding lines, hemming, glue and bolts. For bolt modeling, the use of a tied interface is not necessary, as the shell nodes can be put directly in the rigid bodies.

Note: With a tied interface, the secondary node mass is transferred to the main nodes, if Spot_flag is set to 1. The secondary node inertia is equally distributed over the main nodes by adding mass, so that the induced inertia (at the center of the main surface) is equal to the inertia of the secondary node. If the main surface is a perfect square, the added mass is computed as:

$l_{s} = 4 Δ m \cdot L^{2}$ $l_{s} = 4 Δ m \cdot L^{2}$: $Δ m$ $Δ m$

Added mass

$L$ $L$

Distance between the main node and the center

$l_{s}$ $l_{s}$

Inertia of the secondary node

As long as the secondary node inertia is realistic, the added mass will be very small. A large added mass is observed if the secondary node is too great a distance from the main surface. The ideal is for the secondary node to lie on the main surface plane, right at its center. If this is not the case, the secondary node has inertia at the center of the shell surface:

$l_{s} = m_{s} \cdot L_{s}^{2}$ $l_{s} = m_{s} \cdot L_{s}^{2}$: $m_{s}$ $m_{s}$

Secondary node mass

$L_{s}$ $L_{s}$

Distance between the secondary node and the center

$l_{s}$ $l_{s}$

Inertia of the secondary node

Consequently, a new added mass is set to the main nodes, so that the inertia (due to this new added mass) is equal to the inertia, due to the off-centering of the secondary node.(1)

4 Δ m \cdot L^{2} = m_{s} \cdot L_{s}^{2}

$4 Δ m \cdot L^{2} = m_{s} \cdot L_{s}^{2}$

If Spot_flag=0, there is no added mass, since the secondary node inertia instead is transferred as inertia to the main node. An added inertia that is too large will seriously decrease the accuracy.

Solid Spotweld

Uses 8-node brick element (with /PROP/TYPE43) and /MAT/LAW59+/FAIL/CONNECT (or /MAT/LAW83+/FAIL/SNCONNECT) to model solid spotwelds, which may provide more accurate results.

Solid Element and Property

The brick element uses /PROP/TYPE43 and it has 4 integration points on the shear plane, which is between plane (1, 2, 3, 4) and plane (5, 6, 7, 8). There is one integration point in normal direction t. This element type does not have a time step itself and its stability is ensured by its nodal connections. This means that the thickness of spotweld can be very small. This characteristic is very useful for modeling glue.

Connected to Shell Sheet

/INTER/TYPE2 may be used to connect solid spotwelds with two (upper and lower) main surfaces. Nodes of plane (1,2,3,4) tied on one shell, and nodes of plane (5,6,7,8) tied on another shell. It is not allowed to have any other plane (for example, plane (1,4,8,5)) tied on a shell.

Material and Failure Model

Solid spotwelds in Radioss may be modeled with /MAT/LAW59+/FAIL/CONNECT (or /MAT/LAW83+/FAIL/SNCONNECT). This material model should be validated with four load cases of spotweld tests.

Shear test (angle of loading and spotweld upper surface is 0 degrees below named 0 degree test)
Normal tensile test (90 degree test)
Shear and normal combined test (for example, 30 degree test, 45 degree test or 90 degree test)
Moment test (peel test)

E-Modulus

The stiffness of the spotweld in different tests is different. In the normal test, it is lower than in the shear test, due to deformation of the upper and lower sheets. Therefore, normally the stiffness measured is taken from true stress versus displacement curve of the shear test.

/MAT/LAW59+/FAIL/CONNECT

Material yield curve:
In LAW59, spotweld material yield curves in normal direction and in shear direction are requested. The yield curve (Y_fct_ID_N) in normal direction may be determined from the normal tensile test (90 degree test) and the yield curve (Y_fct_ID_T) in shear direction may be determined from the shear test (0 degree test).

Figure 7.

In this case, the maximum stress is also described inside the curves. Given the reference displacement rate $S R_{r e f}$ $S R_{r e f}$ of the input yield curve, Radioss will consider the displacement rate effect with respect to this reference displacement rate.
Spotweld failure:
Solid spotweld damage and failure may be considered with /FAIL/CONNECT. Displacement criteria and/or energy criteria may be used to describe the failure of the spotweld.
- For displacement criteria, failure occurs when the normal displacement or shear displacement is reached according to 2 alternative behavior types:
  - Uncoupled failure (I_fail=0: uni-directional failure)(2) ${\bar{u}}_{i} \cdot f (\dot{\bar{u}}) > {\bar{u}}_{m a x i}$ ${\bar{u}}_{i} \cdot f (\dot{\bar{u}}) > {\bar{u}}_{m a x i}$
    with $i$ $i$ = 33 for normal direction and $i$ $i$ = 13 or 23 for tangent directions.
    
    In the normal tensile test (90 degree test), element fails once user-defined maximum displacement ${\bar{u}}_{\max N}$ ${\bar{u}}_{\max N}$ is reached.
    
    In the shear tensile test (0 degree test), element fails once user-defined maximum displacement ${\bar{u}}_{\max T}$ ${\bar{u}}_{\max T}$ is reached.
    
    Figure 8.
    
    In a combined mode test (for example, 30 degree test or 60 degree test), failure in the solid spotweld does not consider shear and normal combined stress effect. Failure in each direction is considered separately. The element fails as soon as either of these two stresses reaches its corresponding maximum displacement. To consider combined stresses, instead set I_fail=1 and combined stress effect will be then considered.
  - Coupled failure (I_fail=1: multi-directional failure)(3) ${| \frac{{\bar{u}}_{N}}{{\bar{u}}_{\max N}} \cdot α_{N} \cdot f_{N} ({\dot{\bar{u}}}_{N}) |}^{\exp_{N}} + {| \frac{{\bar{u}}_{T}}{{\bar{u}}_{\max_{T}}} \cdot α_{T} \cdot f_{T} ({\dot{\bar{u}}}_{T}) |}^{\exp_{T}} > 1$ ${| \frac{{\bar{u}}_{N}}{{\bar{u}}_{\max N}} \cdot α_{N} \cdot f_{N} ({\dot{\bar{u}}}_{N}) |}^{\exp_{N}} + {| \frac{{\bar{u}}_{T}}{{\bar{u}}_{\max_{T}}} \cdot α_{T} \cdot f_{T} ({\dot{\bar{u}}}_{T}) |}^{\exp_{T}} > 1$
    With I_fail=1, in combined mode test, the element fails before reaching the maximum stress ${\bar{u}}_{\max N}$ ${\bar{u}}_{\max N}$ or ${\bar{u}}_{\max T}$ ${\bar{u}}_{\max T}$ which is closer to reality. To describe the curve failure surface you need at least 4 different combined tests to fit the parameters $α_{N}, α_{T}, \exp_{N}, \exp_{T}$ $α_{N}, α_{T}, \exp_{N}, \exp_{T}$ .
    
    Figure 9. Failure surface
- For energy criteria, failure occurs when the internal energy in normal direction or internal energy in shear direction is reached, corresponding to maximum internal energy $E N_{\max}, E T_{\max}$ $E N_{\max}, E T_{\max}$ .
  
  Figure 10.
  
  In a combined mode test, element failure is also considered with respect to the multi-direction effect on internal energy. If internal energy in normal direction and in shear direction are input, the element fails, if satisfied via:(4) ${(\frac{E n}{E N_{\max}})}^{N_{n}} + {(\frac{E t}{E T_{\max}})}^{N_{t}} \geq 1$ ${(\frac{E n}{E N_{\max}})}^{N_{n}} + {(\frac{E t}{E T_{\max}})}^{N_{t}} \geq 1$
  
  To input only total internal energy $E I_{\max}$ $E I_{\max}$ , the element fails, if satisfied via:(5) $\frac{E (t)}{E I_{\max}} \geq 1$ $\frac{E (t)}{E I_{\max}} \geq 1$
  
  If both $E I_{\max}$ $E I_{\max}$ and $E N_{\max}, E T_{\max}$ $E N_{\max}, E T_{\max}$ are input, the element fails, due to whichever of these two criteria is reached first.
  
  Both displacement criteria and energy criteria may be defined. The element fails, due to whichever criteria is reached first. The element deletion occurs when one integration point reaches the failure criteria, if I_solid=1 or when all integration points reach the failure criteria, if I_solid=2.
Spotweld softening:
After reaching the failure criteria (either displacement criteria or energy criteria) stress is reduced to 0 directly or may be gradually controlled with parameters $T_{\max}$ $T_{\max}$ and $N_{s o f t}$ $N_{s o f t}$ with:(6) $σ = σ_{f} {(1 - \frac{D}{T_{\max}})}^{N_{s o f t}}$ $σ = σ_{f} {(1 - \frac{D}{T_{\max}})}^{N_{s o f t}}$

Figure 11.

Figure 12 shows the effect of different $T_{\max}$ $T_{\max}$ and $N_{s o f t}$ $N_{s o f t}$ on stress reduction behavior.

Figure 12.

/MAT/LAW83+/FAIL/SNCONNECT

Material yield curve:
In LAW83, the spotweld material curve may be input with fct_ID₁. Where in LAW59 input, two yield curves for normal direction and shear direction are required, LAW83 uses just one curve. This curve should take the yield curve from shear test. Furthermore, the yield curve fct_ID₁ for LAW83 is not defined as true stress versus plastic displacement (as in LAW59), but should be a normalized stress versus plastic displacement curve. Yield stress is normalized by maximum stress which are input as parameters $R_{N}, R_{S}$ $R_{N}, R_{S}$ in LAW83.

Figure 13.

The yield curve is different due to different combinations of normal stress and shear stress in the spotweld. This may be described with parameter $β$ $β$ in LAW83 (it is not considered in LAW59). The normalized yield stress in LAW83 is: (7) $σ_{y} = {[{(\frac{σ_{n}}{R_{N} \cdot f_{N} (1 - α \cdot sym)})}^{β} + {(\frac{σ_{s}}{R_{S} \cdot f_{S}})}^{β}]}^{\frac{1}{β}}$ $σ_{y} = {[{(\frac{σ_{n}}{R_{N} \cdot f_{N} (1 - α \cdot sym)})}^{β} + {(\frac{σ_{s}}{R_{S} \cdot f_{S}})}^{β}]}^{\frac{1}{β}}$

In cases where the moment effect is not considered, the normalized yield stress in LAW83 is:(8) $σ_{y} = {[{(\frac{σ_{n}}{R_{N} \cdot f_{N}})}^{β} + {(\frac{σ_{s}}{R_{S} \cdot f_{S}})}^{β}]}^{\frac{1}{β}}$ $σ_{y} = {[{(\frac{σ_{n}}{R_{N} \cdot f_{N}})}^{β} + {(\frac{σ_{s}}{R_{S} \cdot f_{S}})}^{β}]}^{\frac{1}{β}}$

Figure 14 shows the difference of normalized maximum stress in combined tests between LAW83 and LAW59.

Figure 14.

Figure 15 shows the effect of varying $β$ $β$ on normalized maximum stress in combined tests using LAW83.

Figure 15.

Parameter $α$ $α$ is used to describe the moment effect in the spotweld.

Figure 16. Non-central tensile test (peel test)

Use $α \cdot sym$ $α \cdot sym$ to reduce the maximum stress of peel test. $sym$ $sym$ is the sin of the angle between the spotweld upper surface and lower surface. It is changed during spotweld deformation and is in range of [-1,1]. The $α$ $α$ parameter may be fitted with a simple FEM model to match the real experiment data. ¹

Figure 17. Different $α$ $α$ effects on peel test on force versus displacement

The displacement rate effect on the material yield curve may also be considered with curve inputs fct_ID_N and fct_ID_S.

Material damage and failure:

For spotweld failure, /FAIL/SNCONNECT may be used. In this failure model, the plastic displacement (in both normal and shear directions) of damage beginning and failure are needed.

For a combined mode test, similar to maximum stress in LAW83,

β_{0}

$β_{0}$ is needed to describe plastic displacement at damage beginning and

β_{f}

$β_{f}$ to describe plastic displacement at failure.

For spotwelds with moment (peel test), similar to maximum stress in LAW83,

α_{0}

$α_{0}$ is needed to describe plastic displacement at damage beginning during the peel test and

α_{f}

$α_{f}$ to describe plastic displacement at failure of peel test.

Table 1. General Capability of the Two Spotweld Modeling Approaches
		/MAT/LAW59+/FAIL/CONNECT		/MAT/LAW83+/FAIL/SNCONNECT
Yield curve		Two yield curves (in normal and shear directions)		One normalized yield curve with maximum stress $R_{N}, R_{S}$ $R_{N}, R_{S}$
Maximum stress in combined mode test		Normal and shear effect in combined test not considered.		Use $α$ $α$ to consider normal and shear effect in combined mode tests.
Failure	Failure criteria	Displacement criteria	Uni-direction failure Multi-direction failure	Displacement criteria, Multi-direction failure
	Failure criteria	Energy criteria	Uni-direction failure Multi-direction failure	Displacement criteria, Multi-direction failure
	Failure in combined mode test	Proportionally controlled with $α_{T}, α_{N}, \exp_{T}, \exp_{N}$ $α_{T}, α_{N}, \exp_{T}, \exp_{N}$ in displacement criteria and with $N_{n}, N_{t}$ $N_{n}, N_{t}$ in energy criteria.		Controlled with $β_{0}, β_{f}$ $β_{0}, β_{f}$
	Moment effect (peel test)	No control in input		Controlled with $α_{0}, α_{f}$ $α_{0}, α_{f}$
	Softening	With $T_{\max}, N_{s o f t}$ $T_{\max}, N_{s o f t}$ (stress curve decreases)		With reference to damage displacement and failure displacement (stress linear decrease)

Pasligh, N., Schilling, R., and Bulla, M., "Modeling of Rivets Using a Cohesive Approach for Crash Simulation of Vehicles in Radioss," SAE Int. J. Trans. Safety 5(2):2017, doi:10.4271/2017-01-1472