Breakable bonds, such as spot welds, between surfaces:
can be defined only at the nodes of the secondary surface of a pure main-secondary contact
pair;
can be defined only in the first step of a simulation;
constrain the secondary node to the main surface until the failure criterion of the bond is
met;
are designed to provide a simple simulation of spot weld failure under
relatively monotonic straining, such as occurs during an impact of a vehicle
structure;
do not constrain the rotational degrees of freedom at the node;
use either a time to failure or a damaged failure model to simulate
the postfailure response of the bonds;
A contact pair that contains spot welds must be a pure main-secondary contact pair; therefore,
spot welds cannot be used with single-surface contact. If the contact pair consists of two
deformable surfaces, Abaqus/Explicit would normally use a balanced main-secondary contact pair. In such situations you must
specify a weighting factor (see Contact Formulations for Contact Pairs in Abaqus/Explicit) to define a
pure main-secondary contact pair. Contact pairs containing spot welds must be defined in the
first step of a simulation. The spot welds are located at the nodes of the secondary surface
of the contact pair.
Spot welds can also be modeled more accurately using fasteners instead of
breakable bonds. Fasteners have the advantage of being mesh independent in
their definition and are convenient for defining point-to-point connections
between two or more surfaces with the capability to model plasticity, damage,
and failure behavior. However, fasteners are intended to be used in three
dimensions; therefore, the fastener method cannot be used to specify spot welds
for contact pairs in a two-dimensional case. If non-breakable bonds (rigid spot
welds) are to be modeled, it is recommended that you use the mesh-independent
spot weld feature (Mesh-Independent Fasteners).
All of the secondary nodes which are bonded to a main surface can be grouped together into a node
set.
Adjustments to the Initial Positions of the Bonded Nodes
Nodes that are bonded to a main surface with spot welds should be defined so that they contact
the surface in the model's initial configuration. If the bonded nodes are not in contact
initially, Abaqus/Explicit will enforce the bonded constraint by prescribing strain-free displacements to those
nodes. The nodes will begin the simulation exactly in contact with the main surface. If the
spot welds are defined incorrectly, this automatic adjustment of the nodes may cause the
analysis to end immediately as a result of excessive initial distortion of elements that are
connected to the bonded nodes.
Forces Carried by a Spot Weld
Abaqus
assumes that a spot weld carries a force normal to the surface onto which the
node is welded, ,
and two orthogonal shear forces tangent to the surface,
,
.
The magnitude of the resultant shear force, ,
is defined as .
The normal force is positive in tension.
A spot weld is assumed to be so small that it carries no moments or torque.
As a result, spot welds do not impose any constraints on rotational degrees of
freedom.
Defining the Failure Criterion for the Spot Welds
The failure criterion for a spot weld is defined as
where
is the force required to cause failure in tension (Mode I loading),
is the force required to cause failure in pure shear (Mode
II loading), and
and
are defined above.
A typical yield surface for spot welds is shown in
Figure 1.
By specifying a very large value for either
or ,
the yield criteria of the spot welds can be made independent of either shear
forces or normal forces, as shown in
Figure 2.
Spot weld forces sometimes exhibit significant noise, which can cause the
spot weld to reach its failure criterion when a filtered solution of the spot
weld forces would still be well within the strength limits of the spot weld.
This is characterized by a noisy time history of the BONDSTAT variable and can correspond to an unrealistically early onset
of failure of a spot weld. Two models for deterioration of a spot weld after
the onset of failure are discussed below: a time to failure model and a
postfailure damage model. With the time to failure model a single, spurious
spike in the constraint force history that just exceeds the spot weld strength
will lead to complete failure of the spot weld. The postfailure damage model
may mitigate the effects of noise in the spot weld force.
Defining the Postfailure Behavior of the Spot Welds
Once the constraint forces on a spot weld exceed the failure criterion, the
spot weld fails and deteriorates until the weld is broken completely. The
behavior of the spot weld during this deterioration process can be simulated
using either a damaged failure model or by linearly reducing the constraint
forces to zero over a specified time period. With either model, the applied
constraint forces from a spot weld are limited by the size of the yield surface
as defined by the failure criterion. Deterioration of the spot weld is modeled
by shrinking the yield surface to zero while retaining its original shape.
If the predicted constraint forces exceed the yield surface, the applied
forces are calculated using a radial flow rule to return to the yield surface.
After complete failure, the node behaves like the rest of the secondary nodes in the contact
pair. The node may recontact the main surface, but the weld plays no further role.
Defining the Time to Failure Model
You specify the time to failure, ,
which is the time required for the spot weld to fail completely after the
initial failure criterion has been exceeded. Once failure is detected, the weld
constraint is relaxed linearly over the time .
Abaqus/Explicit
shrinks the yield surface to zero over the time period
:
where t is the time since
Abaqus/Explicit
detected initial failure of the weld.
Defining the Postfailure Damage Model
As stated above, if the predicted constraint forces exceed the failure criterion, the forces
carried by the spot weld are calculated using a radial flow rule to return to the yield
surface. Since the forces in the weld in this case are less than the constraint forces
required to constrain the welded node on the main surface, the welded node will move
relative to the main surface. The work expended during this relative motion is used to
determine how the yield surface degrades.
During failure the behavior of the weld is assumed to be such that any
stretching of the weld in the normal direction, or any shearing of the weld,
dissipates energy.
Abaqus/Explicit
assumes a linear force-displacement relationship after failure, thus resulting
in the behaviors sketched in
Figure 3
when the weld is subjected to pure Mode I or pure Mode
II loading.
More general loadings create combinations of these responses.
You define the amount of energy that the weld can dissipate in Mode I and
Mode II by specifying the breakage
displacements in the normal and shear directions under pure Mode I and Mode
II loading,
and .
Using these linear force-displacement relationships, the failure criterion
for the damaged failure model is
where
is the energy expended in Mode I;
is the energy expended in Mode II;
is the breakage energy in Mode I, which is calculated as
;
and
is the breakage energy in Mode II, which is
calculated as .
Post-Yield Surface Interactions in Spot Welds
Any friction, contact damping, or softening defined at the spot weld will
not affect the analysis until the weld is broken completely; i.e., until the
failure surface has shrunk to zero.
Bead Size of the Spot Weld
The initial bead size of the spot weld, , is taken into account by offsetting the secondary surface node associated
with the spot weld from the main surface by an amount equal to the bead size during the
penetration calculations. A main or secondary surface defined on shell or membrane elements
is itself offset from the midplane of the element by the half-thickness of the shell or
membrane.
If the damaged failure model is chosen to characterize the postfailure behavior, the size of the
spot weld bead may grow due to tensile yielding of the spot weld. The size of the spot weld
is equal to the sum of and the accumulated after the failure of the spot weld. After the weld has broken,
the size of the bead at breakage is taken into account for subsequent contact between the
weld node and the main surface.
Available Output for Spot Welds
Two output variables specifically related to spot welds, the bond status
and bond load, are available.
These variables can be written as history output to the output database
(.odb) file.
Definition of Bond Status
The bond status (output variable BONDSTAT) is a measure of how close a spot weld is to complete failure.
The bond status varies between 0.0 and 1.0 and is defined to be
if the time to failure postfailure model is chosen or
if the damaged failure model is chosen. With either model, the bond status
is equal to 1.0 before the spot weld fails.
Definition of Bond Load
The bond load (output variable BONDLOAD) is a measure of how close the current constraint forces at a
spot weld are to its failure surface. The value of the bond load also varies
between 0.0 and 1.0 and is defined to be
if the damaged failure model is chosen. For the time to failure model, the
bond load is defined to be
prior to failure. Then, the bond load is 1.0 from the moment of first yield
until total failure, at which point the bond load becomes 0.0.
Example: Spot Welds and Output Requests
The spot-welded nodes in node set WELDS are a subset of the
nodes on surface A, which is the secondary surface of the pure
main-secondary contact pair.
NSET, NSET=WELDS
node set definitionCONTACT PAIR, MECHANICAL CONSTRAINT=KINEMATIC,
INTERACTION=A TO B, WEIGHT=0.
secondary surface A, main surface BSURFACE INTERACTION, NAME=A TO B
BOND
WELDS, , , , , ,
OUTPUT, HISTORY, TIME INTERVAL=0.001
CONTACT OUTPUT, NSET=WELDS
BONDSTAT, BONDLOAD
Here
must be specified if the time to failure model is used, or
and
must be specified if the damaged failure model is chosen.