The WoehlerCurve class

class pylife.materiallaws.WoehlerCurve(pandas_obj)[source]

A PylifeSignal accessor for Wöhler Curve data.

Wöhler Curve (aka SN-curve) determines after how many load cycles at a certain load amplitude the component is expected to fail.

The signal has the following mandatory keys:

  • k_1 : The slope of the Wöhler Curve

  • ND : The cycle number of the endurance limit

  • SD : The load level of the endurance limit

The _50 suffixes imply that the values are valid for a 50% probability of failure.

There are the following optional keys:

  • k_2The slope of the Wöhler Curve below the endurance limit

    If the key is missing it is assumed to be infinity, i.e. perfect endurance

  • TNThe scatter in cycle direction, (N_90/N_10)

    If the key is missing it is assumed to be 1.0 or calculated from TS if given.

  • TSThe scatter in cycle direction, (S_90/S_10)

    If the key is missing it is assumed to be 1.0 or calculated from TN if given.

property ND
property SD
property TN

The load direction scatter value TN.

property TS

The load direction scatter value TS.

basquin_cycles(load, failure_probability=0.5)[source]

Calculate the cycles numbers from loads according to the Basquin equation.

Parameters:

  • load (array_like) – The load levels for which the corresponding cycle numbers are to be calculated.

  • failure_probability (float, optional) – The failure probability with which the component should fail when charged with load for the calculated cycle numbers. Default 0.5

Returns:

cycles – The cycle numbers at which the component fails for the given load values

Return type:

numpy.ndarray

basquin_load(cycles, failure_probability=0.5)[source]

Calculate the load values from loads according to the Basquin equation.

Parameters:

  • cycles (array_like) – The cycle numbers for which the corresponding load levels are to be calculated.

  • failure_probability (float, optional) – The failure probability with which the component should fail when charged with load for the calculated cycle numbers. Default 0.5

Returns:

cycles – The cycle numbers at which the component fails for the given load values

Return type:

numpy.ndarray

broadcast(parameter, droplevel=None)

Broadcast the parameter to the object of self.

Parameters:

parameters (scalar, numpy array or pandas object) – The parameter to broadcast to

Returns:

parameter, object

Return type:

index aligned numerical objects

Examples

The behavior of the Broadcaster is best illustrated by examples:

  • Broadcasting pandas.Series to a scalar results in a scalar and a pandas.Series.

    obj = pd.Series([1.0, 2.0], index=pd.Index(['foo', 'bar'], name='idx'))
obj

    idx
foo    1.0
bar    2.0
dtype: float64

    parameter, obj = Broadcaster(obj).broadcast(5.0)

parameter

    array(5.)

    obj

    idx
foo    1.0
bar    2.0
dtype: float64

  • Broadcasting pandas.DataFrame to a scalar results in a pandas.DataFrame and a pandas.Series.

    obj = pd.DataFrame({
    'foo': [1.0, 2.0],
    'bar': [3.0, 4.0]
}, index=pd.Index([1, 2], name='idx'))
obj
    foo bar
    idx
    1 1.0 3.0
    2 2.0 4.0 
    parameter, obj = Broadcaster(obj).broadcast(5.0)

parameter

    idx
1    5.0
2    5.0
dtype: float64

    obj
    foo bar
    idx
    1 1.0 3.0
    2 2.0 4.0

  • Broadcasting pandas.DataFrame to a a pandas.Series results in a pandas.DataFrame and a pandas.Series, if and only if the index name of the object is None.

    obj = pd.Series([1.0, 2.0], index=pd.Index(['tau', 'chi']))
obj

    tau    1.0
chi    2.0
dtype: float64

    parameter = pd.Series([3.0, 4.0], index=pd.Index(['foo', 'bar'], name='idx'))
parameter

    idx
foo    3.0
bar    4.0
dtype: float64

    parameter, obj = Broadcaster(obj).broadcast(parameter)

parameter

    idx
foo    3.0
bar    4.0
dtype: float64

    obj
    tau chi
    idx
    foo 1.0 2.0
    bar 1.0 2.0
cycles(load, failure_probability=0.5)[source]

Calculate the cycles numbers from loads.

Parameters:

  • load (array_like) – The load levels for which the corresponding cycle numbers are to be calculated.

  • failure_probability (float, optional) – The failure probability with which the component should fail when charged with load for the calculated cycle numbers. Default 0.5

Returns:

cycles – The cycle numbers at which the component fails for the given load values

Return type:

numpy.ndarray

Notes

By default the calculation is performed according to the Basquin equation using basquin_cycles(). Derived classes can choose to override this in order to implement a different fatigue law.

fail_if_key_missing(keys_to_check, msg=None)

Raise an exception if any key is missing in a self._obj object.

Parameters:
Raises:

  • AttributeError – if self._obj is neither a pandas.DataFrame nor a pandas.Series

  • AttributeError – if any of the keys is not found in the self._obj’s keys.

Notes

If self._obj is a pandas.DataFrame, all keys of keys_to_check meed to be found in the self._obj.columns.

If self._obj is a pandas.Series, all keys of keys_to_check meed to be found in the self._obj.index.

See also

get_missing_keys(), stresssignal.StressTensorVoigt

property failure_probability
classmethod from_parameters(**kwargs)

Make a signal instance from a parameter set.

This is a convenience function to instantiate a signal from individual parameters rather than pandas objects.

A signal class like

@pd.api.extensions.register_dataframe_accessor('foo_signal')
class FooSignal(PylifeSignal):
    pass

The following two blocks are equivalent:

pd.Series({'foo': 1.0, 'bar': 2.0}).foo_signal

FooSignal.from_parameters(foo=1.0, bar=1.0)
get_missing_keys(keys_to_check)

Get a list of missing keys that are needed for a self._obj object.

Parameters:

keys_to_check (list) – A list of keys that need to be available in self._obj

Returns:

missing_keys – a list of missing keys

Return type:

list

Raises:

AttributeError – if self._obj is neither a pandas.DataFrame nor a pandas.Series

Notes

If self._obj is a pandas.DataFrame, all keys of keys_to_check not found in the self._obj.columns are returned.

If self._obj is a pandas.Series, all keys of keys_to_check not found in the self._obj.index are returned.

property k_1

The second Wöhler slope.

property k_2

The second Wöhler slope.

keys()

Get a list of missing keys that are needed for a signal object.

Returns:

keys – a pandas index of keys

Return type:

pd.Index

Raises:

AttributeError – if self._obj is neither a pandas.DataFrame nor a pandas.Series

Notes

If self._obj is a pandas.DataFrame, the self._obj.columns are returned.

If self._obj is a pandas.Series, the self._obj.index are returned.

load(cycles, failure_probability=0.5)[source]

Calculate the load values from loads.

Parameters:

  • cycles (array_like) – The cycle numbers for which the corresponding load levels are to be calculated.

  • failure_probability (float, optional) – The failure probability with which the component should fail when charged with load for the calculated cycle numbers. Default 0.5

Returns:

cycles – The cycle numbers at which the component fails for the given load values

Return type:

numpy.ndarray

Notes

By default the calculation is performed according to the Basquin equation using basquin_cycles(). Derived classes can choose to override this in order to implement a different fatigue law.

miner_elementary()[source]

Set k_2 to k_1 according Miner Elementary method (k_2 = k_1).

Return type:

modified copy of self

miner_haibach()[source]

Set k_2 to value according Miner Haibach method (k_2 = 2 * k_1 - 1).

Return type:

modified copy of self

miner_original()[source]

Set k_2 to inf according Miner Original method (k_2 = inf).

Return type:

modified copy of self

to_pandas()

Expose the pandas object of the signal.

Returns:

pandas_object – The pandas object representing the signal

Return type:

pd.DataFrame or pd.Series

Notes

The default implementation just returns the object given when instantiating the signal class. Derived classes may return a modified object or augmented, if they store some extra information.

By default the object is not copied. So make a copy yourself, if you intent to modify it.

transform_to_failure_probability(failure_probability)[source]